Question

The outer and the inner radii of a hollow sphere are 12cm and 10cm. Find its volume.
(a) $3050\dfrac{2}{3}c{{m}^{3}}$
(b) $305\dfrac{2}{3}c{{m}^{3}}$
(c) $6050\dfrac{2}{3}c{{m}^{3}}$
(d) None of these

Answer 1

Hint:We will use the formula for finding volume of sphere and then with the help of that we will find the volume of sphere with outer radius and inner radius and then we will subtract these two to get the final answer.

Complete step-by-step answer:
Let’s first write the formula for finding volume of sphere,
Volume of sphere = $\dfrac{4\pi {{r}^{3}}}{3}$ , where r = radius of sphere.
Now we will use the above formula to find the volume of the hollow sphere.
Let R = 12cm outer radius
r = 10cm inner radius
Now the required volume will be,
$\dfrac{4\pi {{R}^{3}}}{3}-\dfrac{4\pi {{r}^{3}}}{3}$
Now we will substitute the values of R and r and find the required volume,
After substituting we get,
$\begin{aligned} & =\dfrac{4\pi \left( {{12}^{3}}-{{10}^{3}} \right)}{3} \\\ & =\dfrac{88\left( 1728-1000 \right)}{21} \\\ & =\dfrac{88\times 728}{21} \\\ & =\dfrac{32032}{7}\times \dfrac{2}{3} \\\ & =3050\dfrac{2}{3}c{{m}^{3}} \\\ \end{aligned}$
Hence option (a) is correct.

Note: We have used the formula for finding the volume of the sphere and then we have subtracted the two volumes by taking the inner and outer radius.The final result is in improper fraction so convert it into mixed fraction and get the value.Students should not make mistake while calculating volume of sphere as they given hollow sphere just we have to take difference of volume of outer and inner radius of sphere or remember the direct formula of volume of hollow sphere $\dfrac{4\pi ({R}^{3}-{r}^{3})}{3}$.