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Name: Period: Foundations of Technology Unit 2 Lesson 5: Prototypes and Modeling File 2.5.3: Calculating Surface Area and Volume Review Date: Calculating Surface Area and Volume Review Directions: Use the appropriate equation to answer the following questions. All answers should be recorded below or in your engineering design journal. Remember to show all work. 1. Find the areas of the following: (a). A square with a width and height equal to 5 feet. (b). A rectangle with a length equal to 8.5 cm and height equal to 6.0 cm. (c).A right triangle with a base equal to 24 in and height equal to 18 in. (d). A circle with a radius equal to 12 feet. ©2013 International Technology and Engineering Educators Association Foundations of Technology, Third Edition / Technology, Engineering, and Design 2. Find the surface area and volume of a storage cube measuring 5 feet on each side. 3. Find the surface area and volume of rectangular prism with a length equal to 15 cm, width equal to 6 cm and a height equal to 7.5 cm. 4. Find the surface area and volume of a basketball with a radius equal to 29.5 inches. If this basketball was filled with water, how much water is needed? ©2013 International Technology and Engineering Educators Association Foundations of Technology, Third Edition / Technology, Engineering, and Design 5. Find the surface area and volume of a cylinder with a diameter equal to 14 cm and a height equal to 10 cm. 6. The ABC box company makes square puzzle cubes that measure 4 inches along each edge. They shipped the cubes in a box 8 in x 12 in x 16 in. How many cubes can they ship in the box? ©2013 International Technology and Engineering Educators Association Foundations of Technology, Third Edition / Technology, Engineering, and Design Name: Period: Foundations of Technology Unit 2 Lesson 5: Prototypes and Modeling File 2.5.3: Calculating Surface Area and Volume Review - ANSWERS Date: Calculating Surface Area and Volume Review Directions: Use the appropriate equation to answer the following questions. All answers should be recorded below or in your engineering design journal. Remember to show all work. 1. Find the areas of the following: (a). A square with a width and height equal to 5 feet. Equation for Area (A) = a² A = (5ft)² A = 25ft² (b). A rectangle with a length equal to 8.5 cm and height equal to 6.0 cm. Equation for Area (A) = W x H A = 8.5cm x 6cm A = 51cm² (c).A right triangle with a base equal to 24 in and height equal to 18 in. Equation for Area (A) = ½(b x h) A = ½(24in x 18in) A = ½(432in²) A = 216in² (d). A circle with a radius equal to 12 feet. Equation for Area (A) = π(r²) A = π(12ft)² A = π(144ft²) A = 452ft² ©2013 International Technology and Engineering Educators Association Foundations of Technology, Third Edition / Technology, Engineering, and Design 2. Find the surface area and volume of a storage cube measuring 5 feet on each side. Equation for Surface Area (SA) = 6a² SA = 6(5ft)² SA = 6(25ft²) SA = 150ft² Equation Volume (V) = a³ V = (5ft)³ V = 125ft³ 3. Find the surface area and volume of rectangular prism with a length equal to 15 cm, width equal to 6 cm and a height equal to 7.5 cm. Equation Surface Area (SA) = 2(L x W) + 2(H x W) + 2(L x H) SA = 2(15cm x 6cm) + 2(7.5cm x 6cm) + 2(15cm x 7.5cm) SA = 2(90cm²) + 2(45cm²) + 2(112.5cm²) SA = 180cm² + 90cm² + 225cm² SA = 495cm² Equation Volume (V) W x H x D V = 15cm x 6cm x 7.5 cm V = 675cm³ 4. Find the surface area and volume of a basketball with a radius equal to 29.5 inches. If this basketball was filled with water, how much water is needed? Equation Surface Area (SA) = 4π(r²) SA = 4π(29.5in)² SA = 4π(870.25in²) SA = 10,935in² ©2013 International Technology and Engineering Educators Association Foundations of Technology, Third Edition / Technology, Engineering, and Design Equation Volume (V) = 4/3π(r³) V = 4/3π(29.5in)³ V = 4/3π(25,672in³) V = 107,536in³ 5. Find the surface area and volume of a cylinder with a diameter equal to 14 cm and a height equal to 10 cm. Equation Surface Area (SA) = 2π(r²) + 2π(r x h) SA = 2π(7cm)² + 2π(7cm x 10cm) SA = 2π(49cm²) + 2π(70cm²) SA = 308cm² + 440cm² SA = 748cm² Equation Volume(V) = π(r²)h V = π(7cm)²(10cm) V = π(49cm²)(10cm) V = 1,539cm³ 6. The ABC box company makes square puzzle cubes that measure 4 inches along each edge. They shipped the cubes in a box 8 in x 12 in x 16 in. How many cubes can they ship in the box? Equation Volume (V) of a Cube = a³ Rubics Cube V = 4in³ Rubics Cube V = 64in³ Equation Volume (V) of a Rectangular Prism = W x H x D Box V = 8in x 12in x 16in Box V = 1,536in³ ©2013 International Technology and Engineering Educators Association Foundations of Technology, Third Edition / Technology, Engineering, and Design # of boxes = box volume = cube volume 1,536in³ 64in³ = 24 cubes per box ©2013 International Technology and Engineering Educators Association Foundations of Technology, Third Edition / Technology, Engineering, and Design