Find the area of the base of a cone whose generatrix is 7 cm long and the lateral surface area is 21n cm2.

To find out the area of the base of a given cone, we will use the formula: Sbot = Π * R ^ 2 = Π * (S side / (Π * L)) ^ 2, where S side is the area of the lateral surface (S side = 21 * Π cm2); L – generatrix length (L = 7 cm).

Let’s perform the calculation: Sbok = Π * (Sbok / (Π * L)) ^ 2 = Π * (21 * Π / (Π * 7)) ^ 2 = Π * 3 ^ 2 = 9Π cm2.

Answer: The base area of a given cone should be 9Π cm2.