Question

A right circular cylinder has a height of ​ 19 3/4 ​ ft and a diameter ​ 1 2/5 ​ times its height. What is the volume of the cylinder? Enter your answer in the box. Use 3.14 for pi and round only your final answer to the nearest hundredth.

Answer 1

Answer:

$V=16,594.15 ft^{3}$

Step-by-step explanation:

The volume of a cylinder is defined as

$V= \pi r^{2} h$

So, by given we know that the diameter of the circular base is $1 \frac{2}{5}$ times its height which is $19 \frac{3}{4}ft$, if we transform each mixed number into a fraction, it would ne

Diameter: $\frac{7}{5}$ times the height.

Height: $\frac{79}{4}ft$

That means,

$d=\frac{7}{5} h$, replacing the height, we have

$d=\frac{7}{5}(\frac{79}{4} ) \\d=\frac{553}{20}$

But, the radius is half the diameter by definition

$r=\frac{d}{2}=\frac{\frac{553}{20} }{2}}=\frac{553}{40} \\r=13\frac{33}{40}ft$

Now that we know the radius and the height, we can use the formula to find the volume

$V= \pi r^{2} h\\V= (3.14)(\frac{553}{40} )^{2}(\frac{553}{20}} )\\ V=16,594.15 ft^{3}$

Therefore, the volume rounded to the nearest hundred is

$V=16,594.15 ft^{3}$