Respuesta :
The volume of a cone that has a circumference of 155 feet and a height of 25 feet is 15,933.34 [tex]feet^3[/tex]
Solution:
We have been given that a cone that has a circumference of 155 feet and a height of 25 feet
We need to find the volume of the cone.
The formula to find the volume of the cone is:
[tex]\text {Volume of cone}=\frac{1}{3} \pi r^{2} h[/tex]
Where "r" is the radius and "h" is the height
Finding the value of radius:
[tex]\begin{array}{l}{\text {circumference of a circle }=2 \pi r} \\\\ {155=2 \pi r} \\\\ {r=\frac{155}{2 \pi}} \\\\ {r=24.67 \mathrm{feet}}\end{array}[/tex]
[tex]\begin{array}{l}{\text {Volume of cone}=\frac{1}{3} \times \pi \times(24.67)^{2} \times 25} \\\\ {=15,933.34 \text { feet }^{3}}\end{array}[/tex]
Therefore, the volume of the cone is 15,933.34 [tex]feet^3[/tex]
