Question

A cone without a base is made from a half-circle of radius 10 cm. Determine the volume of the cone. Explain your reasoning.

Answer 1

Answer:

  125π√3/3 cm³ ≈ 226.72 cm³

Step-by-step explanation:

The length of the circular edge of the half-circle is ...

  (1/2)C = (1/2)(2πr) = πr = 10π . . . . cm

This is the circumference of the circular edge of the cone, so the radius of the cone is found from ...

  C = 2πr

  10π = 2πr . . . . fill in the numbers; next, solve for r

  r = 5 . . . . cm

The slant height of the cone is the original radius, 10 cm, so the height of the cone from base to apex is found from the Pythagorean theorem.

  (10 cm)² = h² + r²

  h = √((10 cm)² -(5 cm)²) = 5√3 cm

And the cone's volume is ...

  V = 1/3·πr²h = (1/3)π(5 cm)²(5√3 cm)

  V = 125π√3/3 cm³ ≈ 226.72 cm³