# Lesson 17

Volume and Density

### Problem 1

The washer in the image has an inner diameter of $$\frac14$$ inch. The outer diameter measures $$\frac34$$ inch, and the washer is $$\frac14$$ inch thick. The density of the metal the washers are made of is 0.285 pounds per cubic inch.

How much do 5 washers weigh, in pounds? Round your answer to the nearest hundredth.

### Solution

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### Problem 2

Assume that a cell is a sphere with radius $$10^{\text-3}$$ or 0.001 centimeter, and that a cell’s density is 1.1 grams per cubic centimeter.

1. Koalas weigh 6 kilograms on average. How many cells are in the average koala?
2. Hippos weigh 1,400 kilograms on average. How many cells are in the average hippo?

### Solution

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### Problem 3

The density of water is 1 gram per cm3. An object floats in water if its density is less than water’s density, and it sinks if its density is greater than water’s. Will a toy in the shape of a rectangular prism that is 1 centimeter by 2 centimeter by 2 centimeter with mass 3 grams sink or float? Explain your reasoning.

### Solution

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### Problem 4

A cube and a sphere both have volume 512 cubic units. Which solid has a greater surface area? Explain your reasoning.

### Solution

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(From Unit 5, Lesson 16.)

### Problem 5

Give the dimensions of 2 solids with equal surface area and different volume.

### Solution

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(From Unit 5, Lesson 16.)

### Problem 6

A right cone has a base with diameter 10 units. The volume of the cone is $$100\pi$$ cubic units. What is the length of a segment drawn from the apex to the edge of the circular base?

A:

5 units

B:

12 units

C:

13 units

D:

15 units

### Solution

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(From Unit 5, Lesson 15.)

### Problem 7

A pyramid has a height of 4 inches and a volume of 40 cubic inches. Select all figures that could be the base for this pyramid.

A:

a 5 inch by 2 inch rectangle

B:

a 3 inch by 10 inch rectangle

C:

a triangle with height 10 inches and base 3 inches

D:

a right triangle with one side 5 inches and the hypotenuse 13 inches

E:

a heart with area 30 square inches

### Solution

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(From Unit 5, Lesson 14.)

### Problem 8

Select all solids for which the formula $$V=Bh$$ applies.

A:

a triangular prism

B:

a triangular pyramid

C:

a square pyramid

D:

a rectangular prism

E:

a cone

F:

a cylinder

### Solution

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(From Unit 5, Lesson 9.)

### Problem 9

Two distinct lines, $$\ell$$ and $$m$$, are each perpendicular to the same line $$n$$. A fourth distinct line, $$k$$, is also perpendicular to line $$n$$. Does line $$k$$ intersect line $$\ell$$ or line $$m$$? Explain how you know.

### Solution

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(From Unit 1, Lesson 6.)