Question
A solid metallic sphere of radius 21 cm is melted and
recast into a number of smaller cones of height 7 cm and base radius 3 cm. How many such cones can be made?Solution
The volume of the sphere = (4/3) * π * (r)^3, where r = 21 cm. Volume of the sphere = (4/3) * π * (21)^3 = (4/3) * π * 9261 = 12348 * π cubic cm. The volume of each cone = (1/3) * π * (r)^2 * h, where r = 3 cm and h = 7 cm. Volume of each cone = (1/3) * π * (3)^2 * 7 = (1/3) * π * 63 = 21 * π cubic cm. Number of cones = 12348 * π / 21 * π = 588.
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