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 length of each side of a cube is 4 cm. What is the volume of the cube?
Option 1: 128 cm3
Option 2: 48 cm3
Option 3: 64 cm3
Option 4: 32 cm3
Question : The volume of a cube is 512 cm3. What is the length of each side of this cube?
Option 1: 9 cm
Option 2: 8 cm
Option 3: 6 cm
Option 4: 12 cm
Question : The largest possible right circular cylinder is cut out from a wooden cube of edge 7 cm. Find the volume of the cube (in cm3) left over after cutting the cylinder. (Use $\pi=\frac{22}{7}$)
Option 1: 73.5
Option 2: 63.5
Option 3: 87.5
Option 4: 67.5
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 : What will be the volume of a sphere with a radius of 65 cm? (approximately)
Option 1: $4.5 \times 10^6 $ cm3
Option 2: $6 \times 10^6$ cm3
Option 3: $1.15 \times 10^6$ cm3
Option 4: $2 \times 10^6$ cm3
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