Explanation
For such sphere its diameter should be equal to the side of sphere.
Diameter of sphere $$= 7$$ cm
So, radius $$= 3.5 $$ cm
Volume of the sphere carved out $$= \dfrac{4}{3}\pi r^3$$
$$=\displaystyle \frac{4}{3}\times \frac{22}{7}\times 3.5^{3}$$
$$= 179.7 cm^3$$
$$\text{Volume of the cube of edge} 'a' \text{units} =a^3 \\= 7^3\\=343$$
$$\text{Volume of the wooden left} = 343 – 179.7 \\= 163.3\ cm^3$$
Total surface area of the hemisphere $$= 462 {cm}^2$$
Total surface area of the hemisphere $$= 2\pi r^2$$
$$\Rightarrow 462 = 3\pi r^2$$
$$\Rightarrow r = 7$$ cm
Volume of hemisphere $$= \dfrac{2}{3}\pi r^3$$
$$V = \dfrac{2}{3}\times \dfrac{22}{7} \times 7^3$$
$$V = 718.67 {cm}^3$$
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