Question

A cone has a volume of 1,570 in^3. If the height of the cone is 15 inches, calculate the radius of the cone.

Answer 1

10 inches

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Use the formula for the volume of a cone:

• V = (1/3)πr²h, where V is the volume, r is the radius of the base, and h is the height of the cone.

Given:

• Volume of the cone, V = 1570 in³
• Height of the cone, h = 15 inches

We rearrange the formula to solve for r:

• r² = (3V) / (πh)

Now, substitute the known values and solve:

• r² = (3 * 1570) / (π * 15)
• r² = (4710) / (47.12388980384689)
• r² ≈ 100

Take the square root of both sides:

• r = √100
• r = 10 inches

Therefore, the radius of the cone is 10 inches.