Multiple choice

A solid metallic cylinder of height 8 cm and radius 7 cm is melted and recast into a cone of height 24 cm. By what % is the lateral surface area of cone more than that of the cylinder ?

  1. 33.3%

  2. 37.5%

  3. 44.4%

  4. 56.2%

  5. 48.8%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Cylinder: V = pi*7^2*8 = 392*pi. Cone: V = 1/3*pi*r^2*24 = 8*pi*r^2. 8*r^2 = 392, r^2 = 49, r = 7. Slant height l = sqrt(7^2 + 24^2) = 25. Lateral Area of Cone = pi*r*l = pi*7*25 = 175*pi. Lateral Area of Cylinder = 2*pi*r*h = 2*pi*7*8 = 112*pi. Increase = (175-112)/112 = 63/112 = 0.5625 = 56.25%.

AI explanation

Equating the volumes of the cylinder (π × 7² × 8) and the cone ((1/3) × π × r² × 24) gives the cone's base radius as 7 cm. The cylinder's lateral surface area is 2 × π × 7 × 8 = 112π, and the cone's slant height is √(24² + 7²) = 25, giving a lateral surface area of π × 7 × 25 = 175π. The percentage increase is ((175π - 112π) / 112π) × 100, which equals (63 / 112) × 100 = 56.25%, making the closest given value 56.2%.

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