Asked in: March 2025 board paperThe radii of the circular ends of a frustum of a cone are 14 cm and 8 cm. If the height of the frustum is 8 cm, find (\(\pi = 3.14\)):(i) Curved surface area of frustum. (ii) Total surface area of the frustum. (iii) Vo…

Answer: (i) 690.8 cm\(^2\) (ii) 1507.2 cm\(^2\) (iii) 3114.88 cm\(^3\)

\(r_1 = 14\), \(r_2 = 8\), h = 8. Slant height \(l = \sqrt{h^2 + (r_1 - r_2)^2} = \sqrt{64 + 36} = \sqrt{100} = 10\) cm.

(i) CSA \(= \pi (r_1 + r_2) l = 3.14 \times 22 \times 10 = 690.8\) cm\(^2\).

(ii) TSA \(= \pi (r_1 + r_2) l + \pi r_1^2 + \pi r_2^2 = 690.8 + 3.14(196 + 64) = 690.8 + 3.14 \times 260 = 690.8 + 816.4 = 1507.2\) cm\(^2\).

(iii) Volume \(= \dfrac{1}{3}\pi h (r_1^2 + r_2^2 + r_1 r_2) = \dfrac{1}{3} \times 3.14 \times 8 \times (196 + 64 + 112)\)

\(= \dfrac{1}{3} \times 3.14 \times 8 \times 372 = 3.14 \times 8 \times 124 = 3114.88\) cm\(^3\).