Question

The volume of the cone is 462 yd.³ The height is 3ft. What is the radius of the cone? use 22/7 for pie

Answer 1

We are asked to determine the radius of a cone given its volume and its height. To do that we will use the following formula for the volume of a cone:

`V=(\pi r^2h)/(3)`

Now, we solve for the radius "r". First, we multiply both sides by 3:

`3V=\pi r^2h`

Now, we divide both sides by pi and the height:

`(3V)/(\pi h)=r^2`

Now, we take the square root to both sides:

`\sqrt{(3V)/(\pi h)}=r`

Now, we convert the height from feet to yards using the following conversion factor:

`1\text{ yd}=\text{ 3ft}`

Multiplying by the conversion factor we get that the height is 1 yd:

Now, we substitute the values:

`\sqrt{(3(462yd^3))/(((22)/(7))(1yd))}=r`

Solving the operations:

`21yd=r`

Therefore, the radius is 21 yd.