Question

Please asap
for 10 points!​

Answer 1

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.