The internal and external radii of a hollow hemispherical bowl are 20 cm and 23 cm respectively. What is the total surface area (in $$cm^{2}$$) of the bowl?

The internal and external radii of a hollow hemispherical bowl are 20 cm and 23 cm respectively.

internal radii = r = 20 cm

external radii = R = 23 cm

Total surface area (in $$cm^{2}$$) of the bowl = $$2\pi\ R^2+2\pi\ r^2+\pi\ \left(R^2-r^2\right)$$

= $$\pi\left(2R^2+2r^2+R^2-r^2\right)$$

= $$\pi\left(3R^2+r^2\right)$$

= $$\pi\left(3\times23^2+20^2\right)$$
= $$\pi\left(3\times529+400\right)$$

= $$\pi\left(1587+400\right)$$

= $$1987\pi$$