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9-12 Integrated Math 3 Unit 1 Lesson 20

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K-5 Math 6-8 Math •9-12 Math

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Integrated Math 1 Integrated Math 2 •Integrated Math 3

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18 Lesson 19 •Lesson 20

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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

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

Problem 2

ForLesson 18: Surface Area and Volume

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.

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 cubic units. What is the length of a segment drawn from the apex to the edge of the circular base?

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
cubic units
400 cubic units

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

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?

Problem 7

ForLesson 6: Scaling and Unscaling

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.

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

Problem 9

ForLesson 15: Building a Volume Formula for a Pyramid

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