Chapter 12, Problem 5PST

To determine

To calculate : The volume of the rocket.

Answer to Problem 5PST

The volume of the rocket would be $280.5i{n}^3$

Explanation of Solution

Given information : A rocket has a diameter of 4 inches. The total height of the rocket is 2 feet 5 inches. And the height of the nosecone is 7 inches.

Formula used : The volume of the cylinder is $\pi r^2{h}_1$ . And the volume of the cone is $\frac{1}{3}(\pi r^2{h}_2)$ . Where $r$ is the radius and $h_1,h_2$ are the height of the cylinder and the cone. And we know the radius is half of the diameter. Also, 1 foot is 12 inches.

Calculation : Calculate the radius.

  $r=\frac{4}{2}=2$ inches

Calculating the height of the cylinder.

The height of the cylinder would be the height of the rocket minus height of the nosecone.

And the height of the rocket is 2 feet 5 inches that is $(2\times 12)+5=27$ inches.

So, the height of the cylinder would be $h_1=27-7=20$ inches.

Now, find the volume of the cylinder.

  $\begin{array}{l}=\pi r^2{h}_1\\ =3.141\times 2^2\times 20\\ =251.2i{n}^3\end{array}$

Calculating the volume of the nosecone.

Plug the height of the nose cone is $h=7$ inches.

  $=\frac{1}{3}(\pi r^2{h}_2)$

  $\begin{array}{l}=\frac{1}{3}(3.141\times 2^2\times 7)\\ =\frac{87.948}{3}\\ =29.3i{n}^3\end{array}$

Now, the total volume of the rocket would be the volume of the cylinder plus the volume of the nosecone.

  $\begin{array}{l}=251.2i{n}^3+29.3i{n}^3\\ =280.5i{n}^3\end{array}$