Multiple choice

Radius and slant height of a solid right circular cone are in the ratio $3:5$. If the curved surface area is $60\pi sq.cm$, then find its total surface area.

  1. $301\cfrac{5}{7}{cm}^{2}$
  2. $31\cfrac{5}{7}{cm}^{2}$
  3. $302\cfrac{5}{7}{cm}^{2}$

  4. None of these
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A Correct answer
Explanation

r/l = 3/5. Let r=3x, l=5x. h = sqrt(l^2 - r^2) = 4x. CSA = pi*r*l = pi*(3x)(5x) = 15*pi*x^2 = 60*pi. So x^2 = 4, x=2. r=6, l=10. TSA = pi*r(r+l) = pi*6*(6+10) = 96*pi = 96 * 3.14159 = 301.59. 301 5/7 is 301.71.

AI explanation

Given the ratio of radius to slant height is 3:5 and the curved surface area is pi * r * l = 60 * pi, we find r * l = 60. Setting r = 3x and l = 5x yields 15x^2 = 60, so x = 2, making the radius 6 cm and the slant height 10 cm. The total surface area formula is pi * r * (l + r), which gives 60 * pi + 36 * pi = 96 * pi, or approximately 301 and 5/7 sq cm.

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