Question

The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is the height. Suppose a box in the shape of a rectangular prism has length (2a + 11), width (5a – 12), and height (a + 6). Which expression represents the volume of the box?

answer choices in pics

Answer 1

10a^3 + 91a^2 + 54a - 792

Answer 2

`V = (10a^3+91a^2+54a-792)`

Explanation:

We have

`V = lwh` (I), and

`l=2a+11` (II)

`w=5a-12` (III)

`h=a+6` (IV)

We substitute the expression (II),(III) and (IV) in (I), that is

V= (2a+11)(5a-12)(a+6), solve the first one terms

`V = (10a^2-24a+55a-132)(a+6)`

`V = (10a^2+31a-132)(a+6)`

`V = (10a^3+31a^2-132a+60a^2+186a-792)`, simplifying

`V = (10a^3+91a^2+54a-792)`