Question

The volume of the aquarium is V = n (2h-3)th cubic inches.This can be written asV = n (2h-3)(2h - 3)hV=(2n h²-3n h)(2h - 3)Multiply the terms to simplify the volume formula.The volume of the aquarium can bewritten as

Answer 1

Given

The volume of the aquarium is,

$\begin{gathered} V=\pi(2h-3)^2h\text{ }cubc\text{ }inches \\ V=\pi(2h-3)(2h-3)h\text{ }cubic\text{ }units \\ V=(2\pi h^2-3\pi h)(2h-3)\text{ }cubic\text{ }units \end{gathered}$

To simplify the volume formula.

Explanation:

It is given that,

$\begin{gathered} V=\pi(2h-3)^2h\text{ }cubc\text{ }inches \\ V=\pi(2h-3)(2h-3)h\text{ }cubic\text{ }units \\ V=(2\pi h^2-3\pi h)(2h-3)\text{ }cubic\text{ }units \end{gathered}$

That implies,

$\begin{gathered} V=(2\pi h^2-3\pi h)(2h-3)\text{ } \\ =(2\pi h^2\times2h)-(3\pi h\times2h)-(2\pi h^2\times3)+(3\pi h\times3) \\ =4\pi h^3-6\pi h^2-6\pi h^2+9\pi h \\ =4\pi h^3-12\pi h^2+9\pi h \end{gathered}$

Hence, the answer is option a) V = 4πh³-12πh²+9πh.