A right circular cone stands on a hemisphere. The base radius of the cone and that of the hemisphere are the same. If the base radius of the cone is two – thirds the height of the cone and the cone is 15 cm high, calculate, correct to three significant figures, the
(i) total volume of the solid
(ii) total surface area of the solid (𝜋 = 22) 7
"base radius of the cone is two – thirds the height of the cone", let the radius
be r
r = 2/3(15) = 10
volume = hemisphere + cone
= (4/3)π(10^3) + (1/3)π(10^2)(15)
= 4000π/3 + 500π
= 5500π/3 cm^3 = appr 5759.6 cm^3
for the surface area of the cone we need the slant height, let it be s
s^2 = 10^2 + 15^2
s = 5√13
SA = π(10)(5√13) + 2π(10^2)
= ..... cm^2