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.

Accepted Solution

Answer:Volume of cylinder is  34833.21 ft³Step-by-step explanation:Given : A right circular cylinder having height [tex]19\frac{3}{4}[/tex] ft and diameter [tex]\frac{12}{5}[/tex] ​times its height. Given : diameter [tex]\frac{12}{5}[/tex] ​times its height that is diameter [tex]\frac{12}{5}[/tex] ​times  [tex]19\frac{3}{4}[/tex]  that isDiameter = [tex]\frac{12}{5} \times \frac{79}{4}[/tex] ​Diameter = [tex]\frac{237}{5}[/tex] ftRadius is half of diameter, Radius = [tex]\frac{1}{2} \times \frac{237}{5}=\frac{237}{10}[/tex] ft[tex]\text{Volume of Cylinder}=\pi r^2h[/tex]Substitute the values, we get,[tex]\text{Volume of Cylinder}= \pi (\frac{237}{10})^2 \times \frac{79}{4}[/tex][tex]\text{Volume of Cylinder}= \times 3.14 \times (23.7)^2 \times 19.75[/tex][tex]\text{Volume of Cylinder}= \times 3.14 \times (23.7)^2 \times 19.75[/tex][tex]\text{Volume of Cylinder}=34833.21[/tex]Thus, volume of cylinder is  34833.21 ft³