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Unit 1, Lesson 20

Volume and Graphing

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Integrated Math 3

Practice

Problem 1
ForLesson 19: Volume and Density
Student Task Statement

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

Student Task Statement

Rectangular prism measures 5 inches by 5 inches by 6 inches. Rectangular prism 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

Student Task Statement

A right cone has a base with radius 4 units. The volume of the cone is 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

Student Task Statement

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
cubic units
400 cubic units

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Problem 5

ForLesson 14: Prisms and Pyramids

Student Task Statement

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

Student Task Statement

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

Student Task Statement

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

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Problem 8

ForLesson 3: Slicing Solids

Student Task Statement

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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Problem 9

ForLesson 15: Building a Volume Formula for a Pyramid

Student Task Statement

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

<p><strong>Rectangular pyramid. Rectangular base shaded and labeled B equals 30. Dotted line from apex to base labeled 10.</strong></p> — Solid A

<p><strong>Cone. Circular base shaded and labeled B equals 30. Dotted line from apex to base labeled 10.</strong></p> — Solid B

<p><strong>Rectangular prism. Base shaded, two side lengths each labeled square root 10. Height labeled 10.</strong></p> — Solid C

<p><strong>Cylinder. Circular base shaded and labeled B equals 25. Height labeled 4.</strong></p> — Solid D

<p><strong>Cone. Circular base shaded and labeled B equals 25. Dotted line from apex to base labeled 4.</strong></p> — Solid E

Solid A
Solid B
Solid C
Solid D
Solid E

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Volume and Graphing

Practice

Problem 1

Student Task Statement

Problem 2

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Problem 3

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Problem 4

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Problem 5

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Problem 6

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Problem 7

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Problem 8

Student Task Statement

Problem 9

Student Task Statement

Lesson 20 Resources