Question

The storage container below is in the shape of a rectangular prism with a height of 6 feet and a length that is 2 feet more than its width.



Recall that the formula for the volume of a rectangular prism is V = l · w · h, where l is the length, w is the width, and h is the height.

Write the equation that represents the volume of the storage container in terms of its width.

A.
V = 6w2 + 12w
B.
V = 6w2 - 12
C.
V = 6w2 + 12
D.
V = 6w2 - 12w

Answer 1

Hello!!

The length is 2 feet (more) than the width - so L = w+2
Volume = (w+2) * w * 6
Using Distributive Property:

(w*w + 2*w) * 6 =
(w^2+2w) *6 =

Distributive Property

w^2 *6 + 2w*6 =

6w^2 +12w

So you're answer issss - - - - A,

Answer 2

Length \(L\) is 2 feet more (thus, addition) than the width \(W\) so\[L=W+2\]The typical formula for volume is length times width times height, or \(LWH\) but you are given a height of 6 feet. So \(H=6\) and we already have an expression for length as previously mentioned. So, after plugging it in, we now have\[\text{Volume }=LWH=(W+2)(W)(6)=6W(W+2)\]Now we apply the Distributive Property:\[(6W\cdot W)+(6W\cdot2)=6W^2+(2\cdot6)W=6W^2+12W\]

Assuming there are squares (exponents) in your answer choices, your response SHOULD be option A.