Unit 1, Lesson 20

Volume and Graphing

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Integrated Math 3

Practice

Problem 1

ForLesson 19: Volume and Density

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

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Problem 2

ForLesson 18: Surface Area and Volume

Rectangular prism $A$ measures 5 inches by 5 inches by 6 inches. Rectangular prism $B$ measures 2 inches by 4 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.

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Problem 3

ForLesson 17: Putting All the Solids Together

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?

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Problem 4

ForLesson 17: Putting All the Solids Together

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?

1300 cubic units
1200 cubic units
$\frac{1300}{3}$ cubic units
400 cubic units

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Problem 5

ForLesson 14: Prisms and Pyramids

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

cube
right rectangular prism
right square prism
oblique square prism

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Problem 6

ForLesson 12: Cross-Sections and Volume

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

Which juice container has the larger volume?

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Problem 7

ForLesson 6: Scaling and Unscaling

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.

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Problem 8

ForLesson 3: Slicing Solids

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.

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

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