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Question 57
The total surface area of a closed hemisphere is 4158 $$cm^{2}$$. What is the diameter of the hemisphere? [Use $$\pi = \frac{22}{7}$$]
Solution
$$\left(7\times\ 3\right)^2\ =\ \left(radius\right)^2$$
radius = 21 cm
diameter of the hemisphere = $$2\times radius$$
=Â $$2\times 21$$
= 42 cm
total surface area of a closed hemisphere =Â $$3\times\ \pi\ \times\ \left(radius\right)^2$$
$$4158=3\times\ \frac{22}{7}\times\ \left(radius\right)^2$$
$$63=\frac{1}{7}\times\ \left(radius\right)^2$$
$$7\times\ 9\times\ 7\ =\ \left(radius\right)^2$$$$\left(7\times\ 3\right)^2\ =\ \left(radius\right)^2$$
radius = 21 cm
diameter of the hemisphere = $$2\times radius$$
=Â $$2\times 21$$
= 42 cm
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