Question

Which group of expressions could represent the dimensions of a rectangular prism with a volume of 2y3 + 15y2 + 28y?

A. y, y + 4, 2y + 7
B. y, y + 7, 2y + 4
C. y, y + 2, 2y + 14
D. y, y + 14, 2y + 2

Answer 1

C. y, y + 2, 2y + 14

Explanation:

Given

`Volume = 2y^3 + 15y^2 + 28y`

Required

Determine which set of dimensions is applicable

The volume of a rectangular prism is calculated as:

`Volume = Length * Width * Height`

So, to solve this question, we have to test each options using the above formula

A. y, y + 4 and 2y + 7

`Volume = y * (y + 4) * (2y + 7)`

Open brackets

`Volume = y * (y * 2y+ 4* 2y + y * y+ 4* 7)`

`Volume = y(2y^2+ 8y + y^2+ 28)`

`Volume = 2y^3+ 8y^2 + y^3+ 28y`

Collect Like Terms

`Volume = 2y^3 + y^3+ 8y^2+ 28y`

`Volume = 3y^3+ 8y^2+ 28y`

B. y, y + 7, 2y + 4

`Volume = y * (y + 7) * (2y + 4)`

Open brackets

`Volume = y * (y * (2y + 4)+ 7* (2y + 4))`

`Volume = y * (2y^2 + 4y+ 14y + 28)`

`Volume = y * (2y^2 + 18y+ 28)`

`Volume = 2y^3 + 18y^2+ 28y`

C. y, y + 2, 2y + 14

`Volume = y * (y + 2) * (2y + 14)`

Open brackets

`Volume = y * (y* (2y + 14) + 2* (2y + 14))`

`Volume = y * (2y^2 + 14y + 4y + 28)`

`Volume = y * (2y^2 + 18y + 28)`

`Volume = 2y^3 + 18y^2 + 28y`

There's no need to check the last option because option c answers the question.

Hence, the dimension is y, y + 2, 2y + 14