Question

The height of a cone is 15 cm. If its volume is 1570 cm³, find the radius of its base.

Answer 1

radius ≈ 10cm

Explanation:

The volume (
`\sf V`) of a cone is given by the formula:

`\sf V = (1)/(3) \pi r^2 h`

Where:

-
`\sf r` is the radius of the base,

-
`\sf h` is the height.

In this case, we're given the height (
`\sf h = 15 \, \text{cm}`) and the volume (
`\sf V = 1570 \, \text{cm}^3`). we need to find the radius (
`\sf r`).

Let's rearrange the formula to solve for the radius (
`\sf r`):

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

Now, substitute the given values:

`\sf r = \sqrt{(3 * 1570)/(\pi * 15)}`

`\sf r = \sqrt{(4710)/(47.1238898)}`

`\sf r \approx √(99.94930426)`

`\sf r \approx 9.997464892 \, \text{cm}`

`\sf r \approx 10 \, \text{cm ( in whole number)}`

Therefore, the radius of the cone's base is approximately
`\sf 10 \, \text{cm}`.