Question : The curved surface area of the sphere is 154 cm2. Find the volume of the sphere (rounded off to one digit after decimal).
Option 1: 156.9 cm3
Option 2: 179.7 cm3
Option 3: 161.1 cm3
Option 4: 147.8 cm3
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Correct Answer: 179.7 cm3
Solution : Given, the curved surface area of the sphere is 154 cm2 Let the radius of the sphere be $r$. $4πr^2 = 154$ ⇒ $4 × \frac{22}{7} × r^2 = 154$ ⇒ $r^2 = \frac{49}{4}$ ⇒ $r = \frac{7}{2}$ So, the volume of the sphere $= \frac{4}{3} × \frac{22}{7} × (\frac{7}{2})^3$ $=\frac{4}{3} × 22 × \frac{49}{8}$ $=11 × \frac{49}{3}$ $=\frac{539}{3}$ $=179.7$ cm$^3$ Hence, the correct answer is 179.7 cm$^3$.
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Question : The volume of a cylinder is 4312 cm3. Its curved surface area is one-third of its total surface area. Its curved surface area (in cm2) is: (Take $\pi=\frac{22}{7}$ )
Option 1: 572 cm2
Option 2: 528 cm2
Option 3: 660 cm2
Option 4: 616 cm2
Question : If the volume of a sphere is 24,416.64 cm3, find its surface area (take $\pi$ = 3.14) correct to two places of decimal.
Option 1: 3069.55 cm2
Option 2: 4069.44 cm2
Option 3: 5096.66 cm2
Option 4: 6069.67 cm2
Question : The volume of the sphere is 38,808 cm3. What is the surface area of the sphere?
Option 1: 4455 cm2
Option 2: 4433 cm2
Option 3: 5544 cm2
Option 4: 3344 cm2
Question : The volume of a right circular cone is 1232 cm3 and its vertical height is 24 cm. Its curved surface area is:
Option 1: 154 cm2
Option 2: 550 cm2
Option 3: 604 cm2
Option 4: 704 cm2
Question : Find the area of the sector of a circle with a radius of 5 cm and an angle of 60° (rounded off to one decimal).
Option 1: 12.8 cm2
Option 2: 14.1 cm2
Option 3: 13.1 cm2
Option 4: 15.1 cm2
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