A hemispherical vessel of radius 14 cm is fully filled with satfully f

1.	A hemispherical vessel of radius 14 cm is fully filled with satfully filled with sand. This sand15 poured on a level ground. The heap of sand forms a cone shapis a cone shape of height7 cm. Calculate the area of ground occupied by the circular bad by the circular base of theheap of the sand.
Answer» Given,Radius of hemisphere r1 = 14 cm Height of cone h = 7 cm Let radius of base of cone = r2 Volume of hemisphere Vh= 2/3pi(r1)^3= 2/3pi(14)^3 Volume of cone Vc= 1/3pir2^2h= 1/3pir2^27 As per given conditionVc = Vh1/3pir2^27 = 2/3pi(14)^3r2^2 = 221414r2 = 214r2 = 28 cm Therefore,Area of base of cone= pir2^2= 22/72828= 22428= 88*28= 2464 cm^2

A hemispherical vessel of radius 14 cm is fully filled with satfully filled with sand. This sand15 poured on a level ground. The heap of sand forms a cone shapis a cone shape of height7 cm. Calculate the area of ground occupied by the circular bad by the circular base of theheap of the sand.

Answer»

Given,Radius of hemisphere r1 = 14 cm

Height of cone h = 7 cm

Let radius of base of cone = r2

Volume of hemisphere Vh= 2/3*pi*(r1)^3= 2/3*pi*(14)^3

Volume of cone Vc= 1/3*pi*r2^2*h= 1/3*pi*r2^2*7

As per given conditionVc = Vh1/3*pi*r2^2*7 = 2/3*pi*(14)^3r2^2 = 2*2*14*14r2 = 2*14r2 = 28 cm

Therefore,Area of base of cone= pi*r2^2= 22/7*28*28= 22*4*28= 88*28= 2464 cm^2