Surface Areas and Volumes — Important Questions

Volume of sphere = 4/3 πr³, Curved surface area of hemisphere = 2πr², Volume of hemisphere = 2/3 πr³, Total surface area of cone = πr(l+r)

The correct formulas are: Volume of sphere = 4/3 πr³, Curved surface area of hemisphere = 2πr², Volume of hemisphere = 2/3 πr³, and Total surface area of cone = πr(l+r). The total surface area of hemisphere is 3πr², not 2πr².

196π cm²

Using the formula 4πr², where r = 7 cm, we get 4π × 7² = 4π × 49 = 196π cm².

l² = r² + h²

By Pythagoras theorem, in a right circular cone, the slant height, height, and radius form a right triangle where l² = r² + h².

A hemisphere has two faces, A hemisphere is half of a sphere, A hemisphere has one curved face and one flat face, The volume of a hemisphere is half the volume of a sphere

A hemisphere is half of a sphere with two faces (one curved, one flat). Its volume is half that of a sphere, but its curved surface area is half the surface area of a sphere (2πr²), not equal to it.