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User Gvee
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Given:

Large cone:

  • r= 8 cm
  • h= 20 cm

Small cone:

  • r= 4 cm
  • h= 10cm

Note that:

  • r: radius
  • h: height

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.


\large\boxed{Formula: V= (1)/(3)\pi{r}^(2)h}

Let's solve!

First, let's find the volume of the smaller cone.

Substitute the values according to the

formula.


V= (1)/(3)×\pi×{4}^(2)×10


V= 167.5516082 \: {cm}^(3)

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.


\boxed{V= 167.55 \: {cm}^(3)}

Next, let's find the volume of the bigger cone.

Substitute the values according to the formula.


V= (1)/(3)×\pi×{8}^(2)×20


V= 1340.412866 \: {cm}^(3)

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.


\boxed{V=1340.41 \: {cm}^(3)}

Now, we can find the volume of the frustum.

We'll have to minus the volume of the smaller cone from the bigger cone.


V= 1340.41-167.55


\large\boxed{V= 1172.86 \: {cm}^(3)}

Hence, the volume of the frustum is 1172.86 cubic centimeters.



User Dilara
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