# Lesson 16

Surface Area and Volume

### Problem 1

These solids all have the same volume. Which has the least surface area?

Solid A

Solid B

Solid C

Solid D

### Solution

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### Problem 2

Rectangular prism \(A\) measures 3 inches by 4 inches by 8 inches. Rectangular prism \(B\) measures 5 inches by 5 inches by 6 inches.

- Before doing any calculations, predict which prism has greater surface area to volume ratio.
- Calculate the surface area, volume, and surface area to volume ratio for each prism.

### Solution

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### Problem 3

Suppose you have 2 pieces of ice with the same volume but in different shapes. If one of the pieces has a greater surface area than the other, it will cool a beverage faster than the ice with less surface area.

- Describe 2 different pieces of ice that have the same volume, but have different surface areas.
- Which piece of ice will cool a beverage faster?

### Solution

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### Problem 4

Suppose this two-dimensional figure is rotated 360 degrees using the vertical axis shown. Each small square on the grid represents 1 square inch. What is the volume of the three-dimensional figure?

### Solution

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(From Unit 5, Lesson 15.)### Problem 5

*Technology required. *A triangular prism has height 8 units. The base of the prism is shown in the image. What is the volume of the prism? Round your answer to the nearest tenth.

### Solution

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(From Unit 5, Lesson 15.)### Problem 6

A cone-shaped container is oriented with its circular base on the top and its apex at the bottom. It has a radius of 12 inches and a height of 8 inches. The cone starts filling up with water. What fraction of the volume of the cone is filled when the water reaches a height of 2 inches?

### Solution

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(From Unit 5, Lesson 14.)### Problem 7

Find the volume of a pyramid whose base is a square with sides of length 4 units and which has a height of 10 units.

### Solution

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(From Unit 5, Lesson 13.)### Problem 8

A solid has volume 4 cubic units and surface area 10 square units. The solid is dilated, and the image has volume 108 cubic units. What is the surface area of the image?

### Solution

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(From Unit 5, Lesson 8.)