Question : What is the volume of the largest sphere that can be carved out of a wooden cube of sides 21 cm?$\left(\pi=\frac{22}{7}\right)$
Option 1: 3851 cm3
Option 2: 6858 cm3
Option 3: 4851 cm3
Option 4: 5821 cm3
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Correct Answer: 4851 cm3
Solution : The largest sphere that can be carved out of a cube of side 21 cm will have a diameter of 21 cm. So, the radius of the sphere, $r$ = $\frac{21}{2}$ cm Now the volume of the sphere = $\frac{4}{3}\pi r^3$ = $\frac{4}{3}×\frac{22}{7}×\frac{21}{2}×\frac{21}{2}×\frac{21}{2}$ = 4851 cm3 Hence, the correct answer is 4851 cm3
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Question : If the surface area of a sphere is $1386 \mathrm{~cm}^2$, then its volume is: (Take $\pi=\frac{22}{7}$ )
Option 1: 8451 cm3
Option 2: 4851 cm3
Option 3: 5418 cm3
Option 4: 4581 cm3
Question : The volume of a sphere of radius 4.2 cm is: (Use $\pi=\frac{22}{7}$)
Option 1: 278.234 cm3
Option 2: 312.725 cm3
Option 3: 297.824 cm3
Option 4: 310.464 cm3
Question : The volume of a right circular cone is 308 cm3 and the radius of its base is 7 cm. What is the curved surface area (in cm2) of the cone? (Take $\pi=\frac{22}{7}$)
Option 1: $22 \sqrt{21}$
Option 2: $44 \sqrt{21}$
Option 3: $22 \sqrt{85}$
Option 4: $11 \sqrt{85}$
Question : A hollow sphere has an outer radius of 6 cm and inner radius of 3 cm. What is the volume of this hollow sphere?
Option 1: 252$\pi$ cm3
Option 2: 356$\pi$ cm3
Option 3: 144$\pi$ cm3
Option 4: 175$\pi$ cm3
Question : The area of the sector of a circle (in cm2) of radius 7 cm and central angle $60^{\circ}$ is: $\left(\right.$Take $\left.\pi=\frac{22}{7}\right)$
Option 1: $\frac{77}{2}$
Option 2: $77$
Option 3: $\frac{77}{3}$
Option 4: $\frac{77}{4}$
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