Question

The external and internal diameters of a spherical shell are 10 cm and 19 cm respectively. Find the volume of material used in the shell.

Answer 1

$\huge\mathfrak{Solution:}$

External diameter of shell = 10 cm

Therefore, external radius of shell R = 5 cm

Internal diameter of the shell = 9 cm

Therefore, internal radius of the shell r = 9/2 = 4.5 cm

Volume of the metal used in the shell = 4/3 × pi × R^3 - 4/3 × pi × r^3

= 4/3 × pi × (R^3 - r^3)

= 4/3 × 22/7 { (5)^3 - (4.5)^3 } cm^3

= 4/3 × 22/7 (125 - 91.125) cm^3

= 88/21 × 33.875 cm^3

= 2981/21 cm^3

= 141.95 cm^3

______________________

HOPE IT HELPS ❤❤

Answer 2

The external radius = 10/2 = 5 cm

Internal radius = 9/2 = 4.5 cm

Volume of material used in the shell

$\frac{4}{3} \times \pi \times ({5}^{3} - {4.5}^{3} ) {cm}^{3} \\ \frac{4}{3} \times \frac{22}{7} \times (125 - 91.125) {cm}^{3} \\ \frac{4}{3} \times \frac{22}{7} \times 33.875 \: {cm}^{3}$

And the correct answer is 141.95 cm^3