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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.

Respuesta :

mhanifa

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.

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