Given:
Large cone:
Small cone:
Note that:
To find:
- The volume of the frustum of the given cone.
Solution:
- Frustum is a part of a cone formed by cutting off the top by a parallel plane.
[tex]\large\boxed{Formula: V= \frac{1}{3}\pi{r}^{2}h}[/tex]
Let's solve!
First, let's find the volume of the smaller cone.
Substitute the values according to the
formula.
[tex]V= \frac{1}{3}×\pi×{4}^{2}×10[/tex]
[tex]V= 167.5516082 \: {cm}^{3}[/tex]
Now, we can round off to the nearest hundredth.
The value in the thousandths place is smaller than 5 so we won't have to round up.
[tex]\boxed{V= 167.55 \: {cm}^{3}}[/tex]
Next, let's find the volume of the bigger cone.
Substitute the values according to the formula.
[tex]V= \frac{1}{3}×\pi×{8}^{2}×20[/tex]
[tex]V= 1340.412866 \: {cm}^{3}[/tex]
Now, we can round off to the nearest hundredth.
The value in thousandths place is smaller than 5 so we won't have to round up.
[tex]\boxed{V=1340.41 \: {cm}^{3}}[/tex]
Now, we can find the volume of the frustum.
We'll have to minus the volume of the smaller cone from the bigger cone.
[tex]V= 1340.41-167.55[/tex]
[tex]\large\boxed{V= 1172.86 \: {cm}^{3}}[/tex]
Hence, the volume of the frustum is 1172.86 cubic centimeters.
