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

A regular pentagonal prism is shown. The apothem of each pentagon is 2.8 centimeters. The height of the prism is (2 x + 1). All sides of the pentagon are congruent.

Which expression represents the volume of the prism, in cubic centimeters?
9x2 + 7x
14x2 + 7x
16x2 + 14x
28x2 + 14x

Respuesta :

the expression that represents the volume of the prism is  14x² + 7x cubic centimeters. Option 2

What is the volume of a pentagonal prism?

The  volume of a pentagonal prism is determined using the formula;

V = 5/2abh

where

  • a is the  apothem
  • h is the height of the prism
  • b is the base of the prism

Now, let's substitute the values given

Let the base be 'x'

The apothem is 2. 8 centimeters

height is 2x + 1

Volume = 5/ 2 × 2. 8 × x × (2x + 1)

Volume = 14/ 2 × x(2x + 1)

Volume = 7x(2x + 1)

Volume = 14x² + 7x

Thus, the expression that represents the volume of the prism is  14x² + 7x cubic centimeters. Option 2

Learn more about a pentagonal prism here:

https://brainly.com/question/27741277

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