Question

4. A cube of side 4 cm contains a sphere touching its sides. Find the approximate volume
of the gap in between.
a. 33.52 cm3.
b. 30.48 cm3
C. 34 cm3.
d. 33 cm3.​

Answer 1

Answer:

Find the gap in between them . =(64-32π3)cm3

Step-by-step explanation:

.

Let ABCD be cube which contain sphere touching its sides.The diameter of sphere is the sides of the cube.

Now,

The volume of the gap in between cube and sphere

The volume of the gap in between cube and sphere= volume of cube -volume of sphere

$\huge \color {red} {4}^{3 } - \frac{4}{3} \times \frac{22}{7} \times ( \frac{4}{2})$

$\implies\huge \color {blue} 64 - \frac{4}{3} \times \frac{22}{7} \times 8 \\ \\ \implies \: \huge \color {green} 64 - \frac{704}{21} \\ \\ \\ \implies \huge \: \frac{1344 - 704}{21} = \frac{640}{21} = 30 \\ \\ \\ \huge \color {red} {30 {cm}^{2} }$