The radii of the ends of a frustum of a solid right-circular cone 45 cm high are 28 cm and 7 cm if this frustum is melted and reconstructed into a solid right circular cylinder whose radius of base and height are in the ratio 3 : 5, find the curved surface area (in cm2) of this cylinder.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 4620.
Area of frustum = 1/3π × h × (r12 + r22 + r1 × r2)
⇒ r1 = 7 cm and r2 = 28 cm
Area of frustum = 1/3π × 45 × (72 + 282 + 7 × 28)
⇒ 1/3π × 45 × (49 + 784 + 196)
⇒ 1/3π × 45 × 1029
Area of cylinder = π × (3x)2 × 5x
Now,
⇒ 1/3π × 45 × 1029 = π × (3x)2 × 5x
⇒ 15 × 1029 = 9x2 × 5x
⇒ 15 × 1029 = 45x3
⇒ x3 = 343
⇒ x = 7 cm
So,
radius of cylinder = 3x = 21 cm
height of cylinder = 5x = 35 cm
C.S.A of cylinder = 2πrh
⇒ 2 × 22/7 × 21 × 35 = 4620 cm2