Question : The total surface area of a solid hemisphere is 1039.5 cm2. The volume (in cm3) of the hemisphere is: (Take $\pi=\frac{22}{7}$)
Option 1: 2425.5
Option 2: 2530.6
Option 3: 2525.6
Option 4: 2225.5
Correct Answer: 2425.5
Solution : Let $r$ be the radius of the hemisphere. We know the total Surface Area of the solid hemisphere = $3\pi r^2$ $⇒3\pi r^2 = 1039.5$ $\Rightarrow 3\times \frac{22}{7}\times r^2 = 1039.5$ $\Rightarrow r^2 = 2.25 \times 7\times 7$ $\Rightarrow r = 10.5 \ \text{cm}$ The volume of the hemisphere = $\frac{2}{3}\pi r^3$ = $\frac{2}{3}\times \frac{22}{7}\times 10.5\times 10.5\times 10.5$ = $ 2425.5 \ \text{cm}^3$ Hence the correct answer is 2425.5 cm3.
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Question : The total surface area of a right circular cylinder is 1848 cm2. The ratio of its total surface area to the curved surface area is 3 : 1. The volume of the cylinder is: (Take $\pi=\frac{22}{7}$)
Option 1: 4312 cm3
Option 2: 3696 cm3
Option 3: 4002 cm3
Option 4: 4851 cm3
Question : The base of the right prism, whose height is 2 cm, is a square. If the total surface area of the prism is 10 cm2, then its volume is:
Option 1: 3 cm3
Option 2: 1 cm3
Option 3: 2 cm3
Option 4: 4 cm3
Question : The ratio of the radius of the base and the height of a solid right circular cylinder is 2 : 3. If its volume is 202.125 cm3, then its total surface area is: (Take $\pi=\frac{22}{7}$)
Option 1: 192.5 cm2
Option 2: 154 cm2
Option 3: 168 cm2
Option 4: 115.5 cm2
Question : The total surface area of a solid hemisphere is 4158 cm2. Find its volume (in cm3).
Option 1: 462
Option 2: 9702
Option 3: 1848
Option 4: 19404
Question : What is the total surface area of a solid right circular cylinder of radius 7 cm and height 8 cm?$(\pi=\frac{22}{7})$
Option 1: 560 cm2
Option 2: 660 cm2
Option 3: 850 cm2
Option 4: 760 cm2
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