A wooden bowl is in shape of a hollow hemisphere of internal radius 9 cm and thickness 1 cm. Find the total surface area of the bowl?

The hemispherical bowl has three surfaces to calculate : the interior hemisphere $$(r_{int} = 9)$$ cm , the exterior hemisphere $$(r_{ext} = 9+1 = 10)$$ cm and the annular(ring shaped) top edge $$(r_{ext} , r_{int})$$

Area of hemisphere = $$2 \pi r^2$$ and area of annular = $$\pi (r^2_{ext} - r^2{int})$$

Total surface area of hemisphere is the sum of these 3 areas

= $$[2 \pi (9)^2] + [2 \pi (10)^2] + [\pi (10^2 - 9^2)]$$

= $$\pi [(2\times81) + (2\times100) + (100 - 81)]$$ 

= $$\pi(162 + 200 + 19) = 381 \pi$$

= $$381 \times \frac{22}{7} = 1197.42$$ $$cm^2$$

=> Ans - (D)