Question

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?
9×2 + 7x
14×2 + 7x
16×2 + 14x
28×2 + 14x

1. hongcuc2
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