A wooden bowl is in shape of a hollow hemisphere of internal radius 8 cm and thickness 1 cm. Find the total surface area of the bowl?

The hemispherical bowl has three surfaces to calculate : the interior hemisphere $$(r_{int} = 8)$$ cm , the exterior hemisphere $$(r_{ext} = 8+1 = 9)$$ 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

= $$[2 \pi (8)^2] + [2 \pi (9)^2] + [\pi (9^2 - 8^2)]$$

= $$\pi [(2\times64) + (2\times81) + (81 - 64)]$$ 

= $$\pi(128 + 162 + 17) = 307 \pi$$

= $$307 \times \frac{22}{7} = 964.85$$ $$cm^2$$

=> Ans - (A)