Question
A right circular cone is surmounted by a hemisphere. The
base radius of the cone is equal to the radius of the hemisphere. The diameter of the hemisphere is 12 cm while the height of the cone is 8 cm. Find the cost of painting the compound object if it costs ₹50 to paint a cm².Solution
Radius = 12 / 2 = 6 cm Since the right circular cone is surmounted on a hemisphere, the area of the base. = 2 π ×62 = 72 π cm² Slant Height = √62 +√82 = 10 cm Hence, the total surface area of the cone is surmounted on the hemisphere. The curved surface area of the cone + the area of the base=π× 6 × 10 + 72π=132π Thus, the cost of painting the compound object = (50 × 132π) / π = 6600 The cost of painting the compound object is ₹6600.
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