A toy is a cone of radius 6 cm and height 7 cm standing on a hemisphere of radius 6 cm. A student reported the volume as 1244.57 cubic centimetres, whereas the correct value is 716.57 cubic centimetres. Which mistake did the student make? (Take π = 22/7.)

Question

Accepted Answer

Used π r^2 h for the cone instead of one-third of π r^2 h. Correct cone = 1/3\π r^2 h = 1/3 × 22/7 × 36 × 7 = 264 cm³ and hemisphere = 2/3\π r^3 = 2/3 × 22/7 × 216 = 452.57 cm³, giving 716.57 cm³. The student's 1244.57 = 792 + 452.57, and 792 is exactly \π r^2 h — three times the correct cone — so the 1/3 was dropped. The hemisphere term 452.57 is already correct, no areas were involved, and the units were centimetres from the start.

A toy is a cone of radius 6 cm and height 7 cm standing on a hemisphere of radius 6 cm. A student reported the volume as 1244.57 cubic centimetres, whereas the correct value is 716.57 cubic centimetres. Which mistake did the student make? (Take π = 22/7.)

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