Question
The total surface area of a right circular cone is twice
the surface area of a sphere having the same radius. If the volume of the sphere is 2304π cm3 , determine the slant height of the cone.Solution
Let the radius of the sphere and the cone be 'r' cm, and the slant height of the cone be 'l' cm. Total surface area of cone = πrl + πr2 Total surface area of sphere = 4πr2 ATQ; 2 X 4πr2 = πr(l + r) Or, 8r = l + r So, 7r = 'l' Volume of sphere = (4/3) πr3 ATQ; 2304π = (4/3) X π X r3 So, 1728 = r3 So, 'r' = 12 cm So, slant height cone = 7r = 7 x 12 = 84 cm
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