Answered

A right circular cylinder has a height of ​ 20 1/2 ​ ft and a diameter ​ 1 1/5 ​ times its height.


What is the volume of the cylinder?

Verified Answer :

kkfreeman14

Answer:

It would be 9,738.54

Step-by-step explanation: For starters, V= r^2(3.14)h

Make things easier by changing 20 1/2 to 20.5)) and 1 1/2 to 1.2))

Now multiply them to get your diameter. 20.5 * 1.20= 24.6.  

You now have a diameter of 24.6. Now, divide 24.6 by 2 to get your radius. So, now you have a radius of 12.3. All you have to do now is plug in your numbers.

V= r^2(3.14)h       V= (12.3)^2 (3.14) 20.5

you should get 9738.5373, but rounding by the hundredths place gets you 9738.54

Do well on your tests guys!

The volume of the cylinder which can be found by the formula \(\pi r^2 h\).

The volume of the given cylinder is 9743.48 cubic feet.

How to calculate the volume of a right circular cylinder?

If the given right circular cylinder has the radius r units and the height being h units, then its volume is given by \(\pi r^2 h\) cubic units.

How to find the volume of the given cylinder if diameter is given?

Diameter is twice of radius, thus radius is half of diameter.

Thus, radius of given cylinder is half of \(1\dfrac{1}{5} times 20\dfrac{1}{2} = \dfrac{6}{5} \times \dfrac{41}{2} = \dfrac{123}{5}\)

=  half of 123/5  = 123/10

feet

Thus, finding the volume of the given cylinder:

\(V = \pi r^2 h = \pi \times (\dfrac{123}{10})^2 \times (20\dfrac{1}{2})\\V \approx 3.14159 \times (12.3)^2 \times (\dfrac{41}{2}) \approx 9743.48 \: \rm ft^3\)

Thus, the volume of given cylinder is 9743.48 cubic feet.

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