Question

4. The difference of the volumes of two spheres is 10,061 cm". If the radius of the smaller sphere be
7 cm, find the difference of the surface areas of the two spheres.​

Answer 1

Sᴏʟᴜᴛɪᴏɴ:

ʟᴇᴛ ᴛʜᴇ ʀᴀᴅɪᴜs ᴏғ ʟᴀʀɢᴇʀ Sᴘʜᴇʀᴇ ʙᴇ  

➩Volume of a Spherical cell = 10,061 cm^3

$\frac{4}{3} \pi({R }^{3} - {r}^{3} ) = 10061 {cm}^{3}$

$\frac{4}{3} \times \frac{22}{7} ( {R}^{3} - {7}^{3} ) = 10061 {cm}^{3}$

$\frac{4}{3} \times \frac{22}{7} ( {R}^{3} - 343) = 10061 {cm}^{3}$

${R}^{3} - 343 = \frac{10061 \times 3 \times 7}{4 \times 22}$

${R}^{3} - 343 = \frac{211281}{88}$

${R}^{3} = \frac{211281}{88} + 343$

${R}^{3} = \frac{211281 + 30184}{88}$

${R}^{3} = \frac{241465}{88}$

$R = \sqrt[3]{ \frac{241465}{88} }$