Question

what is the approximate radius of a cone that has a height of 15 inches and a volume of 1,000 cubin inches

Answer 1

To find the approximate radius of a cone with a given height and volume, we use the formula for the volume of a cone, V = (1/3)πr^2h, to solve for the radius. For a cone with a height of 15 inches and a volume of 1,000 cubic inches, the approximate radius is found to be around 7.978 inches.

Step-by-step explanation:

The question is asking for the approximate radius of a cone with a known height and volume. To find this, we use the formula for the volume of a cone, which is given by

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

where V is the volume, r is the radius, and h is the height of the cone.

Given that the volume (V) is 1,000 cubic inches and the height (h) is 15 inches, we can solve for the radius (r) by rearranging the formula:

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

Plugging in the known values, we get:

`\( r^2 = (3 * 1000)/(\pi * 15) \)\\\\\( r^2 = (3000)/(\pi * 15) \)\\\( r^2 \approx (3000)/(47.1239) \)\\\( r^2 \approx 63.662 \)`

Then, taking the square root of both sides:

`\( r \approx √(63.662) \)\\\( r \approx 7.978 \) inches`

Therefore, the approximate radius of the cone is around 7.978 inches.