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Question 77
The internal and external radii of a hollow hemispherical vessel are 6 cm and 7 cm respectively. What is the total surface area (in cm$$^2$$) of the vessel?
Solution
Total surface area of the vessel = External surface area + internal surface area + upper portion area
r1 = 6 cm
r2 = 7 cm
= $$Â 2 \pi (r2)^2 +Â 2 \pi (r1)^2 +Â \pi ((r2)^2 - (r1)^2)$$
=Â $$\pi[2 \times 7^2 +Â 2 \times 6^2 + (r2)^2 -Â (r1)^2]$$
=Â $$\pi[98 + 72 + 49 - 36] = 183\pi$$
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