Answer:
[tex]V = 11.2 cm^3[/tex]
Step-by-step explanation:
Given
Shape: Right Circular cone
Height, h = 12.5 cm
Base circumference, C = 5.8cm
Required:
Calculate Volume
The volume of a cone is calculated as thus;
Volume, [tex]V = \frac{1}{3}\pi r^2h[/tex]
Where V, r and h represent the volume, the radius and the height of the cone respectively
But first we need to calculate the radius of the cone.
Using formula of circumference.
[tex]C = 2\pi r[/tex]
We have C to be 5.8cm
By substituting this value;
[tex]5.8 = 2\pi r[/tex]
Divide through by [tex]2\pi[/tex]
[tex]\frac{5.8}{2\pi} = \frac{2\pi r}{2\pi}[/tex]
[tex]r = \frac{5.8}{2\pi}[/tex]
[tex]r = \frac{2.9}{\pi}[/tex]
Now, we can calculate the volume of the cone
By substituting [tex]r = \frac{2.9}{\pi}[/tex] and h = 12.5 cm;
[tex]V = \frac{1}{3}\pi r^2h[/tex] becomes
[tex]V = \frac{1}{3}\pi * (\frac{2.9}{\pi})^2 * 12.5[/tex]
[tex]V = \frac{1}{3}\pi * \frac{8.41}{\pi^2} * 12.5[/tex]
[tex]V = \frac{1}{3} * \frac{8.41}{\pi} * 12.5[/tex]
Take [tex]\pi[/tex] as 3.14
[tex]V = \frac{1}{3} * \frac{8.41}{3.14} * 12.5[/tex]
[tex]V = 11.15976[/tex]
[tex]V = 11.2 cm^3[/tex] ---- Approximated
Hence, the volume of the cone is; [tex]V = 11.2 cm^3[/tex]
