Question

A square prism has a height of 12 inches and a base with an area of 30 square inches. A cylinder is inscribed inside the prism. Which statement about the volume of the cylinder, V, is true?

Answer 1

the complete question in the attached figure

we know that

[volume of a square prism]=[area of the base]*h-----> 30*12-----> 360 in³
if a cylinder is inscribed inside the prism
then 
the volume of the cylinder is  V < 360 in³

therefore

the answer is the option
V is less than 360 cubic inches

Answer 2

The volume of the cylinder (282.74 in.³) is less than the volume of the square prism (360 in.³). Then the correct option is C.

What is a rectangular prism?

A rectangular prism is a closed solid that has two parallel rectangular bases connected by a rectangle surface.

What is a cylinder?

A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.

A square prism has a height of 12 inches and a base with an area of 30 square inches.

A cylinder is inscribed inside the prism.

The volume of the square prism will be

$\rm V_{square} = Base \ area * Height\\\\V_{square} = 30 * 12\\\\V_{square} = 360 \ in^3$

The volume of the cylinder will be

$\rm V_{cylinder} = \pi r^2 h$

The radius of the base circle of the cylinder will be

$r = \dfrac{\sqrt{30}}{2}\\\\r = 2.7386$

Then volume will be

$\rm V_{cylinder} = \pi * (2.7368)^2 * 12\\\\V_{cylinder} = 282.74 \ in^3$

The volume of the cylinder (282.74 in.³) is less than the volume of the square prism (360 in.³). Then the correct option is C.

More about the rectangular prism link is given below.

https://brainly.com/question/21308574