The inside of a hemispherical dome of radius 21 $m$ is to be whitewashed at ₹12.50 per $m^2$. What is the cost of the whitewashing, in rupees? Take π = 22/7.

Only the curved inside is whitewashed, so the area needed is the curved surface of a hemisphere, 2π$r^2=2\times (22/7)\times 21^2=2\times 22\times 63=2772m^2$. At ₹12.50 per $m^2$ the cost is $2772\times 12.50$ = ₹34,650. Using π$r^2$ instead — forgetting that a hemisphere has twice the area of the circle it stands on — gives ₹17,325; using the TOTAL surface 3π$r^2$ of a solid hemisphere adds the flat base that is not being whitewashed and gives ₹51,975; treating the dome as a whole sphere, 4π$r^2$, gives ₹69,300.