Volume of Composite Solids and Dimensional Changes

Multiple Choice

Which of the following is a correct method to find the volume of a composite figure made of two rectangular prisms?

• Add the volumes of both prisms together.

• Multiply the volumes of both prisms.

• Subtract the smaller volume from the larger one.

• Divide the total surface area by the height.

Open Ended

Why is it important to understand how to find the volume of composite solids in real-life situations?

Fill in the Blank

The formula for the volume of a sphere is V = ___ πr³.

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Multiple Select

Which of the following solids use the formula V = 1/3 Bh for their volume?

• Prisms

• Pyramids

• Cylinders

• Cones

Math Response

Find the volume of the solid.

Type answer here

Correct Answer: 152.4

Deg^°

Rad

Math Response

Find the volume of the solid.

Type answer here

Correct Answer: 2421

Deg^°

Rad

Math Response

A cylindrical rod for irrigation systems is hollow inside as shown. What is the volume of the cylindrical rod?

Type answer here

Correct Answer: 94.25

Deg^°

Rad

Multiple Choice

If the dimensions of a solid are doubled, by what factor does its volume increase?

• 2

• 4

• 6

• 8

Fill in the Blank

The scale factor used to calculate the change in volume when all dimensions are multiplied by the same number is raised to the power of ___.

Multiple Choice

If the dimensions of a figure are multiplied by 4, how many times larger will the volume be?

• 8 times larger

• 16 times larger

• 64 times larger

• 256 times larger

Multiple Choice

Given a rectangular prism with dimensions 6 in by 2 in by 4 in, if you double the length and width only, what will be the ratio of the new volume to the original volume?

• 2:1

• 3:1

• 4:1

• 8:1

Multiple Choice

If the height of a cylinder is doubled while keeping the base area the same, how does the volume change?

• It doubles

• It triples

• It stays the same

• It is cut in half

Open Ended

Explain how changing only one dimension versus two dimensions of a rectangular prism affects its volume. Use examples from the images to support your answer.

Multiple Choice

If the radius of a cylinder is multiplied by 4, how many times larger will the volume be compared to the original?

• 4 times larger

• 8 times larger

• 12 times larger

• 16 times larger

Multiple Choice

Pyramid A is similar to pyramid B. If the volume of pyramid A is 21 in³ and the volume of pyramid B is 1,344 in³, which of the following is true about the two pyramids?

• Pyramid B is 3 times larger than pyramid A.

• Pyramid B is 4 times larger than pyramid A.

• Pyramid B is 16 times larger than pyramid A.

• Pyramid B is 64 times larger than pyramid A.

Open Ended

Explain the importance of using appropriate units when solving volume problems for different three-dimensional shapes.

Multiple Choice

Which formulas should students apply to solve problems involving the volume of three-dimensional shapes such as prisms, pyramids, cones, cylinders, and spheres?

• Formulas for area of 2D shapes

• Formulas for volume of 3D shapes

• Formulas for perimeter

• Formulas for surface area