Question

Write the formula to find the total surface area of a frustum of a cone​

Answer 1

Answer:

The area of a conical surface of the frustum is the lateral surface area of the frustum. It is equal to one-half of the sum of the circumferences of the bases multiplied by the slant height. The variables C1 and C2 are the circumferences of the bases of the frustum, and l is the slant height. Since C1 = 2πr2 and C2 = 2πr2, replace C by 2πr. For the total surface area, of a frustum of a right circular cone is given by the sum of the lateral surface area and area of the two bases.

LSA = 1/2 (C1 + C2) (l)

LSA = π (r1 + r2) (l)

TSA = π (r1 + r2) (l) + πr12 + πr22

The volume of a frustum of a circular cone is equal to one-third of the sum of the two base areas and the square root of the two base areas, multiplied by the altitude. Since the two bases of a frustum of a cone are circles, you can substitute πr2 to the variable B resulting in a more specific equation of the volume.

V = (1/3) (h) (B1 + B2 + √B1B2)

V = (1/3) (h) [πr12 + πr22 + √(πr12*πr22)]

V = (π/3) (h) (r12 + r22 + r1r2)