Question

The radii of the circular ends of a frustum are 14 cm and 6 cm respectively, and its height is 6 cm. Find its curved surface area. ($\pi = 3.14$)

Hint:

For a frustum, always find the slant height first using $l = \sqrt{(r_1 - r_2)^2 + h^2}$ before calculating surface area.

Answer 1

Step 1: Formula for curved surface area (C.S.A) of a frustum.
\[ \text{C.S.A.} = \pi (r_1 + r_2) l \] where $r_1 = 14$ cm, $r_2 = 6$ cm, and $l$ = slant height.
Step 2: Find slant height using Pythagoras theorem.
\[ l = \sqrt{(r_1 - r_2)^2 + h^2} \] \[ l = \sqrt{(14 - 6)^2 + 6^2} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10 \, \text{cm} \] Step 3: Substitute in the formula.
\[ \text{C.S.A.} = 3.14 \times (14 + 6) \times 10 \] \[ \text{C.S.A.} = 3.14 \times 20 \times 10 = 628 \, \text{sq. cm} \] Step 4: Conclusion.
Hence, the curved surface area of the frustum is 628 sq. cm.
Correct Answer: $628 \, \text{sq. cm}$