Question : The Largest possible sphere is carved out of a cube of side 6 cm. What is the volume of the sphere?
Option 1: $\frac{792}{7}$ cm3
Option 2: $\frac{144}{7}$ cm3
Option 3: $\frac{133}{3}$ cm3
Option 4: $\frac{144}{3}$ cm3
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Correct Answer: $\frac{792}{7}$ cm3
Solution : Side of cube = diameter of sphere = 6 cm ⇒ Radius, $r$ = 3 cm $\therefore$ The volume of the sphere = $\frac{4}{3} \pi r^3$ = $\frac{4}{3}×\frac{22}{7}×3^3$ = $\frac{792}{7}$ cm3 Hence, the correct answer is $\frac{792}{7}$ cm3.
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Question : The volume of a cube is 2.197 cm3. Find the side of the cube.
Option 1: 1.3 cm
Option 2: 1.4 cm
Option 3: 1.1 cm
Option 4: 1.2 cm
Question : Two cubes of iron whose edges are 7 cm and 11 cm are melted and formed into a single cube. Find the volume of the new cube formed.
Option 1: 1881 cm3
Option 2: 1674 cm3
Option 3: 1444 cm3
Option 4: 1221 cm3
Question : The radius of a sphere is 14 cm. What is the surface area of this sphere? [Use $\pi=\frac{22}{7}$]
Option 1: 2464 cm2
Option 2: 1232 cm2
Option 3: 1848 cm2
Option 4: 616 cm2
Question : If the volume of a cube is 5832 cm3, then what is the lateral surface area of this cube?
Option 1: 1024 cm2
Option 2: 384 cm2
Option 3: 576 cm2
Option 4: 1296 cm2
Question : The outer radius of a spherical shell is 13 cm and the thickness of the shell is 3 cm. What is the volume of the metal used for the shell? $\left(\pi=\frac{22}{7}\right)$
Option 1: 1197 cm3
Option 2: 2197 cm3
Option 3: 3024 cm3
Option 4: 5016 cm3
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