Answer to Question #154702 in Geometry for tine

Question

A right circular cone is inscribed in a cube having an edge which measures 20 cm. Find the lateral area and volume of the cone

Answer 1

Solution

For cone inscribed in a cube with edge a=20 cm its diameter d=a and height h=a.

So volume V = (1/3)*A_B*h = (1/3)*(π*d²/4)*h = π*d²*h/12 = π*a³/12 = π*20³/12 = π*2000/3 ≈ 2094.4 cm³  (A_B is area of the cone base).

The slant height of a right circular cone $L=\sqrt{(d/2)^2+h^2}=a\sqrt{5}/2$

Lateral area $LSA=\pi d L/2= \pi a^2 \sqrt{5}/4 \approx 702.48 cm^2$

Answer

volume V = π*a³/12 ≈ 2094.4 cm³

lateral area $LSA= \pi a^2 \sqrt{5}/4 \approx 702.48 cm^2$