Lesson 18

Volume and Graphing

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Problem 1

A cube with side length 5 centimeters has a density of 3 grams per cubic centimeter. What is its mass?

Solution

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(From Unit 5, Lesson 17.)

Problem 2

Rectangular prism \(A\) measures 5 inches by 5 inches by 6 inches. Rectangular prism \(B\) measures 2 inches by 4 inches by 6 inches.

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

Solution

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(From Unit 5, Lesson 16.)

Problem 3

A right cone has a base with radius 4 units. The volume of the cone is \(16\pi\) cubic units. What is the length of a segment drawn from the apex to the edge of the circular base?

Solution

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(From Unit 5, Lesson 15.)

Problem 4

A right pyramid has a square base with sides of length 10 units. Each segment connecting the apex to a midpoint of a side of the base has length 13 units. What is the volume of the pyramid?

A:

1300 cubic units

B:

1200 cubic units

C:

\(\frac{1300}{3}\) cubic units

D:

400 cubic units

Solution

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(From Unit 5, Lesson 15.)

Problem 5

A solid can be constructed with 2 squares and 4 congruent, non-rectangular parallelograms. What is the name of this solid?

A:

cube

B:

right rectangular prism

C:

right square prism

D:

oblique square prism

Solution

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(From Unit 5, Lesson 12.)

Problem 6

Diego is deciding which of 2 juice containers he should buy. One container is in the shape of a cylinder with radius 2.5 centimeters and height 10.5 centimeters. The second container is in the shape of a rectangular prism. The prism also has height 10.5 centimeters. Its length is 4 centimeters and its width is 6 centimeters.

Which juice container has the larger volume?

Solution

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(From Unit 5, Lesson 10.)

Problem 7

A parallelogram has an area of 1 square centimeter. Write an equation where \(y\) is the scale factor required for a dilation of the parallelogram to have an area of \(x\) square units. Sketch a graph representing the equation.

Solution

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(From Unit 5, Lesson 5.)

Problem 8

Suppose several solids are divided into thin slices, all in the same direction. For each set of slices, decide what kind of solid they came from.

  1. a set of similar rectangles, decreasing in size to a single point, ordered from greatest in size to smallest
  2. a set of congruent triangles
  3. a set of congruent squares
  4. a set of circles, decreasing in size to a single point, ordered from greatest in size to smallest

Solution

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(From Unit 5, Lesson 2.)

Problem 9

Four solids on the list have the same volume. Select these solids.

Solid A

Rectangular pyramid. Rectangular base shaded and labeled B equals 30. Dotted line from apex to base labeled 10.

Solid B

Cone. Circular base shaded and labeled B equals 30. Dotted line from apex to base labeled 10.

Solid C

Rectangular prism. Base shaded, two side lengths each labeled square root 10. Height labeled 10.

Solid D

Cylinder. Circular base shaded and labeled B equals 25. Height labeled 4.

Solid E

Cone. Circular base shaded and labeled B equals 25. Dotted line from apex to base labeled 4.

 

A:

Solid A

B:

Solid B

C:

Solid C

D:

Solid D

E:

Solid E

Solution

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(From Unit 5, Lesson 13.)