The correct option is
B 84π cm2 Observe from the figure that the total surface area of a hemispherical shell is the sum of the inner curved surface area, outer curved surface area and the area of the ring.
Given, inner diameter of the shell = 6 cm
So, inner radius(r) = 3 cm
Therefore, inner curved surface area of the shell
=
2πr2 =
2π×32 =
18π cm2 Given, outer diameter of the shell = 10 cm
So, outer radius of the shell(R) = 5 cm
Therefore, outer curved surface area of the shell
=
2πR2 =
2π×52 =
50π cm2 Now, inner radius of the ring is 3 cm and outer radius of the ring is 5 cm.
Therefore, area of the ring
=
π(R2−r2) =
π(52−32) =
16π cm2 ∴ Total surface area = Inner curved surface area + Outer curved surface area + Area of the ring
=
50π cm2 +
18π cm2 +
16π cm2 =
84π cm2