Question

Boxes hold various numbers of square-based prisms in a single column. The square base of each prism has a side length of 18 inches. The height of each prism, h, can be found using the function , where V is the volume of the prism. The total height of the box, b, can be found using the function b(h) = xh, where x is the number of square-based prisms in a specific box. Which function can be used to find the height of a box containing 4 square prisms, depending on the volume of the prisms?

Answer 1

Answer:

$b(V) = \frac{V}{108}$

Step-by-step explanation:

The square base of each prism has a side length of 18 inches. The height of each prism, h, can be found using the function, where V is the volume of the prism.

So, V = 18² × h = 324h

⇒ h = $\frac{V}{324}$ .......... (1)

Now, given that the total height of the box, b, can be found using the function b(h) = xh, where x is the number of square-based prisms in a specific box.

Therefore, the box having 4 square prism will have height

b(h) = 3h

⇒ b(V) = $3 \times \frac{V}{324}$ {From equation (1)}

⇒ $b(V) = \frac{V}{108}$ (Answer)