Question

A right circular cylinder has a height of 22 1/4 ft and a diameter 2 2/5 times its height. What is the volume of the cylinder? Enter your answer as a decimal in the box. Use 3.14 for pi and round only your final answer to the nearest hundredth.

Answer 1

Answer:

The volume of cylinder is:

49806.06 ft^3

Step-by-step explanation:

We are given a right circular cylinder with:

Height(h)=$22\frac{1}{4}ft=\dfrac{89}{4}ft$

and a diameter is $2\frac{2}{5}$ times it's height.

i.e. $\dfrac{12}{5}$ times it height.

i.e. the diameter is given as:

$\dfrac{12}{5}\times \dfrac{89}{4}=\dfrac{267}{5}ft.$

We know that the radius of cylinder is half the diameter.

Hence, radius(r) of cylinder is:

$\dfrac{1}{2}\times \dfrac{267}{5}\\\\=\dfrac{267}{10}$

The volume(V) of cylinder is given by:

$V=\pi r^2h$

$V=3.14\times (\dfrac{267}{10})^2\times \dfrac{89}{4}\\\\V=\dfrac{19922423.94}{400}\\\\V=49806.06ft^3$

Hence, the volume of cylinder is:

49806.06 ft^3