Question

A cone has a volume of 3533.5 cubic inches and a radius of 15 inches. What is its height?

Answer 1

h=14.9966

Explanation:

1. The formula of the volume is:

V=
`(ab(h))/(3)`

2. So you have to substitute the the data that you have:

3533.5
`in^(3)`=
`(ab(h))/(3)`

3. To have the area of the base (ab) you have to get the formula of the circle's area and solve:

A=
`\pi`(
`r^(2)`)

A=
`\pi`(
`15^(2)`)

A=3.1416(225)

A=706.86in

4. Now you have the area of the base:

3533.5
`in^(3)`=
`(706.86(h))/(3)`

5. In this step you are going to clear the variable which is the heigh (h) and solve as an equation:

3533.5
`in^(3)`=
`(706.86(h))/(3)`

3533.5
`in^(3)`(3)=706.86(h)

`(10,600.5)/(706.86)`=h

h=14.9966

The result may vary depending on the value of
`\pi` that you use,

Answer 2

• 15 in

Explanation:

Volume of the cone:

• V = 1/3πr²h

Given:

• V = 3533.5 in³
• r = 15 in

Find the value of h:

• h = 3V/(πr²)

Substitute the values and calculate:

• h = 3*3533.5/(3.14*15²)
• h = 15 in