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Name ______Period ______Comparing &

Use surface area and volume calculations to solve the following situations.

1. Find the surface area and volume of each . Which two have the same surface area? Which two have the same volume?

4 in. 22 in. 10 in. C A 11 in. B 18 in. 10 in. 6 in. 10 in. 6 in.

2. Sketch and label two different rectangular prisms that have the same volume. Find the surface area of each.

3. Do the following have the same surface area, the same volume, or the same surface area and volume?

r = 4 cm r = 2 cm

h = 9 cm h = 24 cm

4. A has a surface area of 125.6 mm2 and a volume of 100.48 mm3. If another cylinder has a radius of 5 mm and the same volume, what would be the height?

5. A cylinder has a radius of 9 yd and a height of 3 yd. A second cylinder has a radius of 6 yd and a height of 12 yd. Which statement is true? a. The cylinders have the same surface area and the same volume. b. The cylinders have the same surface area and different . c. The cylinders have different surface and the same volume. d. The cylinders have different surface areas and different volumes.

6. The surface area of a rectangular prism is 2,116 mm2. If you double the length, width, and height of the prism, what will be the surface area of the new prism? How much larger is this amount?

7. The volume of a cylinder is 14.13 cm3. If you quadruple the radius and the height of the cylinder, what will the volume of the new cylinder be? How much larger is this amount?

8. If the radius and height of a cylinder are multiplied by 6, how will the surface area change?

9. If the length, width, and height of a rectangular prism are multiplied by 5, how will the volume change? a. It will become 5 times greater. b. It will become 15 times greater. c. It will become 25 times greater. d. It will become 125 times greater.

10. Find the surface area and volume of the following rectangular prism.

4 in.

2 in.

12 in.

SA = ______

V = ______

If the dimensions of the rectangular prism are multiplied by 5, how will the surface area and volume be affected?

11. Kudos came up with a new flavor! The problem is that the grocery stores aren’t going to give them any more shelf space to accommodate the additional boxes. They need a new box that has the same volume, but smaller surface area. The current box is 2” x 8” x 12”. Propose dimensions for a new box design.