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The length of the side of a cube is 2.8 cm. What is the volume of the largest sphere that can be taken out of the cube?
Answer & Solution
Correct Answer:
Option
A
Side of cube = 2.8 cm
Then radius of sphere $$ = \frac{{2.8}}{2} = 1.4{\text{ cm}}$$
Because, sphere be taken out of the cube.
⇒ Volume of sphere $$ = \frac{4}{3}\pi {r^3}$$
$$\eqalign{ & = \frac{4}{3} \times \frac{{22}}{7} \times 1.4 \times 1.4 \times 1.4 \cr & = \frac{{88 \times 0.392}}{3} \cr & = \frac{{34.496}}{3} \cr & = 11.498 \cr & = 11.50{\text{ c}}{{\text{m}}^3} \cr} $$
Then radius of sphere $$ = \frac{{2.8}}{2} = 1.4{\text{ cm}}$$
Because, sphere be taken out of the cube.
⇒ Volume of sphere $$ = \frac{4}{3}\pi {r^3}$$
$$\eqalign{ & = \frac{4}{3} \times \frac{{22}}{7} \times 1.4 \times 1.4 \times 1.4 \cr & = \frac{{88 \times 0.392}}{3} \cr & = \frac{{34.496}}{3} \cr & = 11.498 \cr & = 11.50{\text{ c}}{{\text{m}}^3} \cr} $$
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