Question

if the surface area of asphere is 144πm^2then its volums is​

Answer 1

Step-by-step explanation:

Surface area of sphere =4πr

2

⇒4πr

2

=144π

⇒r=

4

144

=

(

2

12

)

2

=6m

⇒ Volume =

3

4

πr

3

=

3

4

×π×6

3

=288πm

3

.

Hence, the answer is (288π)m

3

.

Answer 2

Surface area of sphere =

$\sf \: {144\pi m}^{2}$

• First Find radius...

$\sf \: 144\pi = {4\pi r}^{2} \\ \sf144 \cancel{\pi} = 4 \cancel{\pi} {r}^{2} \\ \sf \: 144 = 4 {r}^{2} \\ \sf {r}^{2} = \frac{144}{4} \\ \sf {r}^{2} = \frac{ \cancel{144}}{ \cancel{4}} = \frac{36}{1} = 36 \\ \sf \:r = \sqrt{36} \\ \sf \: r = 6$

Now...

$\sf \huge \pink{volume \: of \: sphere \: = \frac{4}{3} \pi {r}^{3} }$

$\sf \: = \frac{4}{3} \pi {r}^{3} \\ \sf = \frac{4}{3} \times \frac{22}{7} \times 6 \times 6 \times 6 \\ \sf = \frac{4}{ \cancel{ {3}}^{1} } \times \frac{22}{7} \times \cancel{ {6}}^{2} \times 6 \times 6 \\ \sf = \frac{88}{7} \times 72 \\ \sf = \frac{6336}{7} = {905.14m}^{3} (approx)$