Volume of Solids

Fill in the Blanks

The formula for the volume of a prism is V =

× h, where B is the area of the base and h is the height.

Multiple Choice

Which of the following is the correct formula for finding the volume of a triangular prism?

• V = (Area of triangle) × height

• V = (Area of rectangle) × height

• V = (Area of pentagon) × height

• V = (Area of trapezoid) × height

Math Response

Find the Volume of the prism.

Type answer here

Correct Answer: 62.9

Deg^°

Rad

Multiple Select

Which of the following solids use the formula V = Bh to find their volume?

• Rectangular prism

• Triangular prism

• Regular pentagonal prism

• Triangular pyramid

Open Ended

Explain how the formulas for the volume of prisms and pyramids are similar and how they differ. Provide examples using specific shapes.

Dropdown

The volume of a pyramid is found by multiplying the area of the base by the height and multiplying by​

Select answer

Multiple Choice

What is the formula for the volume of a pyramid?

• V = Bh

• V = 1/3 Bh

• V = πr²h

• V = 4/3 πr³

Math Response

Find the volume for pyramid.

Type answer here

Correct Answer: 1121.76

Deg^°

Rad

Math Response

Find the volume for pyramid.

Type answer here

Correct Answer: 27

Deg^°

Rad

Multiple Choice

Which of the following best explains why the formulas for the volume of a prism and a cylinder are similar?

• Both have circular bases.

• Both have two congruent bases and use the area of the base times the height.

• Both use π in their formulas.

• Both have only one base.

Open Ended

Compare the volume formulas for a cylinder and a sphere. What do you notice about the similarities and differences in their formulas?

Math Response

Find the Volume

Type answer here

Correct Answer: 318.09

Deg^°

Rad

Math Response

Find the Volume

Type answer here

Correct Answer: 113097.34

Deg^°

Rad

Fill in the Blanks

The volume of a sphere is

times the volume of a cone with the same radius and with a height equal to the diameter of the sphere.

Fill in the Blanks

The volume of a rectangular prism can be found by multiplying the length, width, and

.

Open Ended

Explain how you would determine the volume of a solid if you are only given its surface area.

Multiple Select

Which three statements are true about the volumes of a cylinder, a cone, and a sphere?

• The volume of a cone is half the volume of a sphere with the same radius and a diameter equal to the height of the cone.

• The volume of a cone is three times the volume of a sphere with the same radius and a diameter equal to the height of the cone.

• The volume of a sphere is twice the volume of a cone with the same radius and a height equal to the diameter of the sphere.

• The volume of a sphere is two thirds of the volume of a cylinder with the same radius and a height equal to the diameter of the sphere.

• The volume of a cylinder is two thirds of the volume of a sphere with the same radius and a diameter equal to the height of the cylinder.