Question

Using v=lwh, what is an expression for the volume of the following prism?

Answer 1

we know that

The volume of the prism is equal to

$V=L*W*H$

where

L is the length side of the base of the prism

W is the width side of the base of the prism

H is the height of the prism

In this problem we have

$L=\frac{d-2}{3d-9}=\frac{d-2}{3(d-3)}$

$W=\frac{4}{d-4}$

$H=\frac{2d-6}{2d-4}=\frac{2(d-3)}{2(d-2)}=\frac{(d-3)}{(d-2)}$

Substitute the values in the formula

$V=\frac{d-2}{3(d-3)}*\frac{4}{d-4}*\frac{(d-3)}{(d-2)}=\frac{4}{3(d-4)}=\frac{4}{3d-12}$

therefore

the answer is the option

$\frac{4}{3d-12}$

Answer 2

Answer:

Option C is correct

$\frac{4}{3d-12}$

Step-by-step explanation:

Using the formula:

$V = lwh$

where,

l is the length of the prism

w is the width of the prism

h is the height of the prism.

As per the statement:

From the given figure:

Length of the prism(l) = $\frac{d-2}{3d-9}$

Width of the prism(w) = $\frac{4}{d-4}$

Height of the prism(w) = $\frac{2d-6}{2d-4}$

Substitute these in [1] we have;

$V = \frac{d-2}{3d-9} \cdot \frac{4}{d-4} \cdot \frac{2d-6}{2d-4}$

$V = \frac{d-2}{3(d-3)} \cdot \frac{4}{d-4} \cdot \frac{2(d-3)}{2(d-2)}$

⇒$V = \frac{1}{3} \cdot \frac{4}{d-4} \cdot \frac{2}{2}$

Simplify:

⇒$V = \frac{4}{3(d-4)}$

⇒$V = \frac{4}{3d-12}$

Therefore, the expression for the volume of the following prism is, $\frac{4}{3d-12}$