Main Idea and New Vocabulary Key Concept Surface

Main Idea and New Vocabulary Key Concept: Surface Area of Similar Solids Example 1: Surface Area of Similar Solids Example 2: Surface Area of Similar Solids Key Concept: Volume of Similar Solids Example 3: Volume of Similar Solids Example 4: Real-World Example

• Solve problems involving similar solids. • similar solids

Surface Area of Similar Solids The surface area of a rectangular prism is 90 square inches. What is the surface area of a similar prism that is larger by a scale factor of 5? S. A. = 90 × 52 Multiply by the square of the scale factor. S. A. = 90 × 25 Square 5. S. A. = 2, 250 in 2 Simplify. Answer: The surface area is 2, 250 in 2.

The surface area of a rectangular prism is 34 square feet. What is the surface area of a similar prism that is 2 times as large? A. 36 ft 2 B. 68 ft 2 C. 136 ft 2 D. 1, 156 ft 2

Surface Area of Similar Solids STATUE The surface area of a pyramid-shaped statue is 160 square meters. If a scale model is of the statue’s actual size, what is the surface area of the model in square centimeters? Multiply by the square of the scale factor. Square

Surface Area of Similar Solids Simplify. Convert square meters to square centimeters. = 4, 000 cm 2 Simplify. Answer: The surface area of the model is 4, 000 cm 2.

DISPLAYS An ice cream shop has a 4 -foot tall ice cream cone that is displayed inside the store. The cone has a surface area of 2, 318 square inches. A 1 regular ice cream cone is __ the size of the display. 8 What is the surface area of the regular ice cream cone? Round to the nearest tenth if necessary. A. 30. 0 in 2 B. 36. 2 in 2 C. 144. 9 in 2 D. 289. 8 in 2

Volume of Similar Solids A triangular prism has a volume of 96 cubic feet. If the prism is reduced to one half its original dimensions, what is the volume of the new prism? Multiply by the cube of the scale factor. Cube V = 12 ft 3 . Simplify. Answer: The volume of the new prism is 12 cubic feet.

A triangular prism has a volume of 162 cubic feet. If the prism is reduced to one third its original dimensions, what is the volume of the new prism? A. 486 ft 3 B. 54 ft 3 C. 18 ft 3 D. 6 ft 3

SOUP A jumbo-size can of tomato soup is about 3 times the size of a standard-sized can of soup. The standard can has the dimensions shown. Find the surface area and volume of the jumbo-size can.

Find the volume and surface area of the standard soup can first. V = r 2 h ≈ (3. 14)(3. 25)2(10) ≈ 331. 67 cm 3 S. A. = 2( r 2) + 2 rh ≈ 2(3. 14)(3. 25)2 + 2(3. 14)(3. 25)(10) ≈ 66. 33 + 204. 1 ≈ 270. 43 cm 2

Find the volume and surface area of the jumbo-size soup can using the scale factor. V = V(3)3 S. A. = S. A. (3)2 ≈ (331. 67)(3)3 ≈ (270. 43)(3)2 ≈ 8, 955 cm 3 ≈ 2, 434 cm 2 Answer: The jumbo-size soup can has a volume of about 8, 955 cubic centimeters and a surface area of about 2, 434 square centimeters.

PACKAGING A moving company has boxes of various sizes for packing. The smallest box available has the dimensions shown below. Find the surface area and volume of a larger box that is 3 times as large. 12 in. A. S. A. = 2, 592 in 2; V = 5, 184 in 3 B. S. A. = 3, 456 in 2; V = 6, 912 in 3 C. S. A. = 7, 776 in 2; V = 15, 552 in 3 D. S. A. = 7, 776 in 2; V = 46, 656 in 3 12 in.