Question

A cylindrical candle of diameter 8cm and height 7cm is lit. After burning, a hemispherical
depression of diameter 4cm is left in the candle. Find the volume and surface area of this
partially burnt candle.

Answer 1

cylinder:
volume = πr^2 h = 112π
area = 2πr^2 + 2πrh = 88π
hemisphere:
volume = 2/3 πr^3 = 16π/3
area = 4πr^2 = 16π
so the remaining candle has
volume = 112π - 16π/3
original volume minus the hemisphere
area = πr^2 + 2πrh + 2πr^2 + (16π-4π)
that is, the original bottom + lateral + (top - hole)

Answer 2

volume = πr^2 h = 112π
area = 2πr^2 + 2πrh = 88π
hemisphere:
volume = 2/3 πr^3 = 16π/3
area = 4πr^2 = 16π
so the remaining candle has
volume = 112π - 16π/3
original volume minus the hemisphere
area = πr^2 + 2πrh + 2πr^2 + (16π-4π)
that is, the original bottom + lateral + (top - hole)

Answer 3

Wtf