Question

The volume of a rectangular prism is given by the expression10x3 + 46x2 – 21x – 27. The area of the base of the prism is given by the expression 2x2 + 8x – 9. Which of the following expressions represents the height of the prism? (V = Bh)

a) 8x - 3
b) 3x - 5
c) 5x + 3
d) 42x + 3

Answer 1

height = volume / area of the base
= 10x^3 + 46x^2 - 21x - 27 / 2x^2 + 8x - 9

10x^3 / 2x^2 = 5x so the first term in the answer will be 5x

Answer is (c).

Answer 2

The correct option is c.

Explanation:

The volume of a rectangular prism is given by the expression

`V=10x^3+46x^2-21x-27`

The area of the base of the prism is given by the expression

`B=2x^2+8x-9`

The volume of a rectangular prism is

`V=Bh`

Where, B is base area and h is height of the prism. Divide both the sides by B.

`(V)/(B)=h`

So, the height of the prism is

`h=(V)/(B)=(10x^3+46x^2-21x-27)/(2x^2+8x-9)`

Factories the numerator.

`h=( (5 x + 3)(2 x^2 + 8 x - 9) )/(2x^2+8x-9)`

Cancel out the common factors.

`h=5 x + 3`

The height of the prism is 5x+3. Therefore the correct option is c.