The largest possible sphere is carved out of a wooden solid cube of side 7 cm. Find the volume of the wood left. (Use π=227)

Given that, a largest possible sphere is carved out of a wooden solid cube of side

7 cm .

Diameter of sphere,

d = 7 cm

.
Radius of sphere

= \frac{diameter}{2}

\Rightarrow r = \frac{7}{2} cm

Volume of the sphere,

= \frac{4}{3} π r^{3}

[π = \frac{22}{7}]

\Rightarrow

Volume of the sphere,

= \frac{4}{3} \times \frac{22}{7} \times {(\frac{7}{2})}^{3}

\Rightarrow Volume of  the sphere = \frac{4}{3} \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times \frac{7}{2}

\Rightarrow Volume of  the sphere = 179.67 c m^{3}

Volume of a cube

= a^{3}

{\Rightarrow (7)}^{3}

\Rightarrow 7 \times 7 \times 7

\Rightarrow 343 {cm}^{3}

Volume of wood left = Volume of a cube - Volume of the sphere.

Volume of wood left = 343 - 179.67

Volume of wood left = 163.33 c m^{3}

.
Hence the correct option is 2.

The largest possible sphere is carved out of a wooden solid cube of side $7 cm$ . Find the volume of the wood left. (Use $π = \frac{22}{7}$ )