Question

A prism is created using 2 regular pentagons as bases. The apothem of each pentagon is 2.8 centimeters.Which expression represents the volume of the prism, in cubic centimeters?

Answer 1

The question is missing the options and the the drawing of the prism. Here is the complete question and the drawing is in the attachment.

A prism is created using 2 regular pentagons as bases. The apothem of each pentagon is 2.8 centimeters.

Which expression represents the volume of the prism, in cubic centimeters?

a) 9x² + 7x

b) 14x² + 7x

c) 16x² + 14x

d) 28x² + 14x

Answer: b) 14x² + 7x

Step-by-step explanation: The formula to calculate the volume of a prism is:

V = Ab*h

Where

Ab is area of the base

h is the height of the prism

The base is a regular pentagon, which means that all the 5 sides of it is the same. The apothem of a pentagon is a line segment from the center of the pentagon to its side. The area is:

Ap = $\frac{Pa}{2}$

where:

P is perimeter

a is apothem

Area of base:

Ab = $\frac{Pa}{2}$

Ab = $\frac{5x.2.8}{2}$

Ab = 7x

h = 2x+1

Volume of the prism:

V = Ab.h

V = 7x.(2x+1)

V = 14x² + 7x

The expression that represents the volume of this prism is V = 14x² + 7x cubic inches.