problem solving with surface area homework 5 answer key

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Surface Area Worksheets

Surface area worksheets comprise an enormous collection of exercises on different solid figures. The large chunk of exercises is categorized based on a step-by-step approach involving counting unit squares to determine the SA, finding the surface area of nets, and then computing the surface area of geometrical shapes like cubes, cones, cylinders, rectangular prisms, L-shaped prisms, spheres, hemispheres, pyramids, and composite figures, catering to the needs of students in 5th grade through high school. Revisiting surface area is easy with our mixed 3D shapes revision pdfs. Count on our free printable SA worksheets for a great start!

List of Surface Area Worksheets

• Surface Area of 3D Figures Using Nets
• Surface Area by Counting Squares
• Surface Area of Cubes
• Surface Area of Rectangular Prisms
• Surface Area of L-Shaped Prisms
• Surface Area of Triangular Prisms
• Surface Area of Cylinders
• Surface Area of Prisms and Cylinders
• Surface Area of Cones
• Surface Area of Spheres and Hemispheres
• Surface Area of Pyramids
• Surface Area of Mixed Solid Shapes
• Surface Area of Composite Figures

Explore the Surface Area Worksheets in Detail

Surface Area of 3D Figures Using Nets Worksheets

Finding the surface area of 3D figures using nets worksheets assist students in visualizing the surface of solid shapes whose nets are sketched on grids. Add on to their practice in determining the SA of the nets of 3D shapes like cylinders, cones, and pyramids, and in drawing the nets of solid figures too.

Surface Area by Counting Squares Worksheets

Start off with counting unit squares on an isometric paper, follow up by drawing the correct number of squares, and then find the SA of rectangular prisms by counting the squares scaled to varied units. These interesting exercises make the surface area by counting squares pdfs a compulsive print for your grade 5 and grade 6 students.

Surface Area of Cubes Worksheets

Page through these surface area of a cube exercises to practice computing the total area occupied by the cubes with edge length offered as integers, decimals and fractions. Included here are pdfs to find the missing edge length using the SA and more.

Surface Area of Rectangular Prisms Worksheets

Surface area of rectangular prisms handouts are a sure-fire hit in every grade 6, grade 7, and grade 8 geometry curriculum. Find the SA using the height, width, and length, and extend your practice to finding the missing dimensions as well.

Surface Area of L-Shaped Prisms Worksheets

Lay a strong foundation in decomposing shapes with these printable surface area of L-shaped rectangular prism worksheets. Solve for surface area of independent 3D shapes, add them, and subtract the area of the face that connects the rectangular blocks.

Surface Area of Triangular Prisms Worksheets

Expedite practice calculating the surface area of triangular prisms with these worksheet pdfs, rendering the attributes of the triangular bases and rectangular side faces of the figure, in integers and decimals.

Surface Area of Cylinders Worksheets

The surface area of a cylinder pdfs feature solid shapes, each made up of a curved surface with two circular bases. Recall the formula for SA of a cylinder, plug in the integer, decimal, or fractional radius measures in the formula 2πrh + 2πr 2 and compute.

Surface Area of Prisms and Cylinders Worksheets

A mix of rectangular prisms, triangular prisms, and cylinders is what these printable worksheets have in store for your middle and high school learners. Consider memorizing the SA formulas, apply the one relevant to the solid shape, substitute the dimensions and solve.

Surface Area of Cones Worksheets

Give your 6th grade, 7th grade, and 8th grade students an edge over their peers with these surface area of cones exercises. Supplying the values of the dimensions in the formula and calculating the surface area of cones is all that is expected of learners.

Surface Area of Spheres and Hemispheres Worksheets

Build fluency and competence with this collection of surface area of spheres and hemispheres worksheets. Get students to find the TSA of the hemispheres and CSA of the spheres by substituting the dimensions in relevant formulas.

Surface Area of Pyramids Worksheets

Handle these printable surface area of pyramid practice sheets with great dexterity. Learn the know-how of finding the surface area of pyramids applying relevant formulas and substituting the dimensions accordingly.

Surface Area of Mixed Solid Shapes Worksheets

How well do your 8th grade and high school students remember the SA formulas of solid shapes like cubes, cones, cylinders, spheres, hemispheres, prisms and pyramids? Check for yourself with these surface area of solid shapes revision pdfs.

Surface Area of Composite Figures Worksheets

Tee up to decompose each combined shape, find the sum of the SA of individual 3D shapes, subtract the area of the common parts, and determine the SA like a pro with this set of printable surface area of composite shapes worksheets.

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Surface Area Worksheets

This page has worksheets for calculating the area of rectangular prisms and other solid shapes.

Level: Basic (Rectangular Prisms & Cubes Only)

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Level: Intermediate (Rectangular & Rectilinear Prisms)

Level: advanced (pyramids, cylinders, prisms, spheres).

Find the area of squares, rectangles, triangles, and circles. Includes basic, intermediate, and advanced-level worksheets.

Learn to solve operations in order: parenthesis, exponents, multiply & divide, add & subtract.

This page has geometry activities related to circles. Pupils find the area, circumference, radius, and/or diameter.

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Surface Area Worksheet

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Give your grade 6 to 8 students skills and applied questions on surface area.

• 15 questions in total; 10 skills questions and 5 applied questions.
• Answer key included with the related common core standard.
• Print off and share with your classes to support their learning.
• Covers ‘Geometry’: 6.G.A.4

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Into Math Grade 7 Module 11 Lesson 4 Answer Key Solve Multi-step Problems with Surface Area and Volume

We included  HMH Into Math Grade 7 Answer Key PDF   Module 11 Lesson 4 Solve Multi-step Problems with Surface Area and Volume to make students experts in learning maths.

HMH Into Math Grade 7 Module 11 Lesson 4 Answer Key Solve Multi-step Problems with Surface Area and Volume

I Can solve multi-step surface area and volume problems.

Step It Out

Question 1. The surface area of a cube is 24 square inches. What is its volume? Answer: 64 cubic inches. Explanation: Surface area = 6 x s in 2 24 sq in = 6 x s in 2  s = 24/6 = 4 in Volume = s  in 3 Volume = 4 x 4 x 4 = 64 in 3 The volume is  64 cubic inches.

Question 2. A triangular prism with an equilateral triangle as its base has a volume of 64.98 cubic centimeters, a base area of 10.83 square centimeters, and a triangle edge length of 5 centimeters. What is the surface area of the prism in square centimeters? Answer: 111.66 cm 2 Explanation: V = 64.98 cubic centimeters, B = 10.83 square centimeters, Volume of triangular prism = Bh Substitute known values: 64.98 = (10.83) h Divide both sides by 64.98 : 10.83 = h The height of both prism is 6 cm. S = 2B +Ph S = 2 x 10.83 + 15 x 6 S =  21.66 + 90 S = 111.66 cm 2

On Your Own

B. What is the approximate volume of the prism? Answer: 257.4 in 3 . Explanation: Volume = Bh ≈ 23.4 × 11 = 257.4 in 3 The volume is approximately 257.4 in 3 .

B. What is the volume of the composite figure? Answer: 27 ft 3 Explanation: the volume of a prism is V = B h V = 15.6 x 3 = 46.8 sq ft the volume of a cube is V = a 3 V = 3 x 3 x 3 = 27 ft 3 the volume of the composite figure = 46.8 + 27 = 73.8 ft 3

Question 5. Social Studies The USDA estimates that 15 million households in the United States were food insecure in 2017. To help people in their community who might be food insecure, a school has a fundraiser to fill a truck with canned goods for the local food bank. If the cube-shaped boxes used to store the canned goods have a surface area of 24 square feet and the truck will hold 128 boxes, what is the maximum volume of canned goods the students can transport? A. What is the edge length of 1 box? Answer: 2 ft Explanation: Surface area of 24 square feet and the truck A = 6a 2 24 = 6 a 2 Dividing by 6 on both sides 4 = a 2 a = 2 ft B. What is the volume of canned goods that the truck can carry? Answer: 1024 ft 3 Explanation: V = a 3 volume of one box V = 2x 2 x 2 = 8 ft 3 total volume for 128 box V = 128 x 8 = 1024 ft 3

Question 6. A cube has volume 216 cubic inches. Find the surface area of the cube. Answer: 216 sq Explanation: V = a 3 216 = a 3 a = 6 cu in A = 6a 2 A = 6 (6×6) = 216 in 2 216 sq in the surface area of the cube

Question 7. A triangular prism has a triangular base with an area of 6 square centimeters and a perimeter of 12 centimeters. The volume of the triangular prism is 18 cubic centimeters. What is the surface area of the prism? Answer: 48 cu cm Explanation: B = 6 sq cm V = Bh h = V/B =18/6 = 3cm P = 12 cm V = 18 cu cm SA = 2B + Ph SA = 2×6  + 12 x 3 SA = 12 + 36 SA = 48 cu cm

B. Use Structure What is the total volume of all the ice in the tray? Answer: 15 cu in Explanation: V = 1 cu in 15 cubes V = 15 cu in

Question 9. Attend to Precision Maribelle decorates molds for making candles. The molds have the shape of open-topped regular pentagonal prisms. Each mold holds an approximate volume of 275 cubic centimeters of wax. The area of the base of a mold is approximately 27.5 square centimeters and the edge length of the base is 4 centimeters. What is the approximate surface area of a mold (not including a top)? V = 275 cu cm B = 27.5 sq cm l = 4 cm P = 4 x 5 = 20 cm A. What is the approximate height of a mold? Answer: 10 cm Explanation: V = Bh h = V/B h = 275/27.5 h = 10 cm

B. How should the formula for surface area be changed for this situation? Answer: 255 cu cm Explanation: SA = 2B + Ph SA = 2 x 27.5 + 20 x 10 SA = 55 + 200 SA = 255 cu cm

C. What is the approximate surface area of a mold? Answer: 255 cu cm Explanation: SA = 2B + Ph SA = 2 x 27.5 + 20 x 10 SA = 55 + 200 SA = 255 cu cm

Question 11. Reason A rectangular prism has a 10-inch by 2-inch base and a surface area of 424 square inches. What is the volume of a column of 8 rectangular prisms with these dimensions, stacked base-to-base? Answer: l = 10 in w = 2 in A = 20in SA = 424 sq in SA = V = ?

B. What formula will find the space inside the tent? What is the space inside the tent? Answer: 109.89 cu ft Explanation: V = B h V = 15.6 x 7.04 V = 109.89 cu ft

Question 13. Use Structure Kristoff has a wooden cube with a volume of 1,000 cubic inches. He is going to make paper signs for each face of the cube for advertising. A. What is the edge length of the wooden block? Answer: 10 inches Explanation: V = 1000 cu in V = a x a x a V = 10 x 10 x 10 a = 10 in

B. What amount of paper will he need for the signs? Answer: 600 sq in Explanation: SA = 6 x a x a SA = 6 x 10 x 10 SA = 600 sq in Question 14. Use Structure A company stores supplies in cube-shaped boxes in a warehouse. They are stored on pallets that hold 4 boxes wide, deep, and high. The total volume of boxes is 512 cubic feet. Find the surface area of 1 box. A. What is the volume of one cube? What is its edge length? Answer: Edge length 2 feet; volume is 6 cubic feet Explanation: V= length x width x height 512 =length x width x height = 8 x 8 x 8 4 box = 8 ft length 1 box = 2 ft length and width surface area of 1 box is SA = 6 x length x width SA = 6 x 2 x 2 SA = 24 sq ft

B. What is the surface area of one box? Answer: 24 sq ft Explanation: 1 box = 2 ft length and width surface area of 1 box is SA = 6 x length x width SA = 6 x 2 x 2 SA = 24 sq ft

Question 15. A trapezoidal prism has a volume of 585 cubic centimeters. The area of the base is 39 square centimeters. If the base has sides measuring 4, 6.5, 6.5, and 9 centimeters, what is the surface area of the prism? Answer: 468 sq cm Explanation: V = 585 cubic centimeters. B = 39 square centimeters. P = 4 + 6.5 + 6.5 + 9 = 26 cm V = Bh 585 = 39 h h = 585 / 39 = 15 cm SA =2B + Pl SA = 2 x 39 + 26 x 15 SA = 78 + 390 = 468 sq cm

Lesson 11.4 More Practice/Homework

Question 1. Use Structure Holly is using wood to build the base and sides of a regular hexagonal prism-shaped herb garden with a volume of 4.3875 cubic feet. The area of the base is 5.85 square feet, and the side length of the hexagon is 1\(\frac{1}{4}\) feet long. Find the amount of wood Holly will need to complete the project. V = 4.3875 sq ft area of the base is 5.85 square feet B = 5.85 square feet length L = 1\(\frac{1}{4}\) feet = 1.25 ft P= 6 x 1\(\frac{1}{4}\) = 6 x \(\frac{5}{4}\) = 7.5 feet

A. What is the height of the herb garden? Answer: 0.75 ft Explanation: V = Bh h = 4.3875  / 5.85 h =  0.75 ft

B. What amount of wood, in square feet, does Holly need? Answer: 18.75 sq ft Explanation: SA = 2B +Ph SA = 2 x 4.3875 + 7.5 x 1.25 SA = 8.775 + 9..375 SA = 18.75 sq ft

A. What is the edge length of one box? Answer: 360/45 = 8

B. What is the surface area of one layer of boxes on the floor of the truck bed? Answer:

C. How many boxes make up this one layer? Answer:

Question 3. A regular hexagonal prism has a surface area of 1,714.56 square centimeters. If the area of the base is 665.28 square centimeters and the side length is 16 centimeters, what is the volume of the prism? Answer:

Question 4. A cube has a surface area of 96 square inches. If 16 cubes are combined to make a rectangular prism, what is the volume of the rectangular prism? Answer: Given, A cube has a surface area of 96 square inches. Surface Area = 6a² 6a² = 96 a² = 96/6 a = 4 in Volume of a cube = a³ V = 4³ V = 64 cu. in Volume of a prism = 64 × 16 V = 1024 cu. in

Question 6. A cube has a surface area of 1,176 square inches. What is the volume of the cube? (A) 14 in 3 (B) 196 in 3 (C) 1,728 in 3 (D) 2,744 in 3 Answer: Option(D) Explanation: SA = 6 a 2 1176/6 = a 2 196 =  a 2 a = 14 V = a x a x a = 14 x 14 x  14 v = 196 x 14 =  2744 in 3

Question 7. Ina makes cakes in a pan shaped like a rectangular prism. The base of the pan is an 8-inch by 12-inch rectangle, and the volume of the pan is 288 cubic inches. Find the surface area of a cheesecake baked in this pan. Answer: Given, Ina makes cakes in a pan shaped like a rectangular prism. The base of the pan is an 8-inch by 12-inch rectangle, and The volume of the pan is 288 cubic inches. 12 × 8 × h = 288 cu. in 96 × h = 288 h = 288/96 h = 3 Surface area = LW + LH + WH SA = 96 × 2 + 12 × 6 + 8 × 8 SA = 192 + 72 + 64 SA = 328 sq. in

Question 8. Suppose you are given the base area and surface area of a triangular prism and the side lengths of the triangular base. Select all the steps needed to find the volume of the prism. (A) Find the height of the prism using the surface area formula. (B) Find the height of the prism using the volume formula. (C) Find the height of the triangle. (D) Use the area of the base and the height to find the volume. (E) Use the height of the base and the height of the prism to find the volume. Answer: Step 1: Find the height of the prism using the surface area formula. (perimeter of the base × length of prism) + (2 ×  base area) Step 2: Use the height and area base to find the volume V = Area base × height Option A and D are the correct answers.

Spiral Review

Question 9. How many triangles can be drawn with side lengths 8 feet, 10 feet, and 21 feet? Answer: No, because the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. 8 + 10 = 18 18 < 21 So, it is not possible to draw triangles with side lengths of 8 feet, 10 feet, and 21 feet.

Question 10. Jared works as a landscaper. He installs a sprinkler that sprays water in a circle with an 8-foot radius. What is the approximate area covered by the sprinkler? Use 3.14 for π. Answer: Given, Jared works as a landscaper. He installs a sprinkler that sprays water in a circle with an 8-foot radius. Area of circle = πr² A = 3.14 × 8 × 8 A = 3.14 × 64 A = 200.96 sq. ft Thus the area covered by the sprinkler is 200.96 ft²

Question 11. A bike wheel has a 16-inch diameter. Approximately how far will the wheel travel in three rotations? Use 3.14 for π. Answer: Given, A bike wheel has a 16-inch diameter. 3 rotations = 3 × 16 × π 3 × 16 × 3.14 = 150.72 ≈ 151 inches

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Unit 9 – Volume and Surface Area of Solids

The Volume and Surface Area of Prisms

LESSON/HOMEWORK

LECCIÓN/TAREA

LESSON VIDEO

EDITABLE LESSON

EDITABLE KEY

SMART NOTEBOOK

The Circumference and Area of a Circle

Cylinders and Their Volumes

The Surface Area of a Cylinder

Cones and Their Volumes

Unit Review

Unit 9 Review

UNIT REVIEW

REPASO DE LA UNIDAD

EDITABLE REVIEW

Unit 9 Assessment Form A

EDITABLE ASSESSMENT

Unit 9 Assessment Form B

Unit 9 Exit Tickets

Unit 9 Mid-Unit Quiz – Form A

Unit 9 Mid-Unit Quiz – Form B

U09.AO.01 – Basic Volume Practice

EDITABLE RESOURCE

U09.AO.02 – Practice with Surface Area of Prims and Cylinders

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Surface Area Homework Worksheet with Answer Key

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Included you will receive notes on an introduction to surface area. The purchase will include the student note sheet and also the answer key. The guided notes I use in my classroom include lots of additional information with helpful tips for students to use to give them important information to help them learn the material. I always include students to have a highlighter when we take guided notes. This homework sheet goes over identifying three-demensional shapes and identifying how many faces they have, along with matching nets to the three-dimensional shape.

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