Question

Find the volume of sphere whose surface area is 154cmsquare

Answer 1

Hey there !!

Given that, surface area of sphere = 154 cm²

4 πr² = 154
4 × 22 / 7 × r² = 154
r² = 154×7 / 4×22
r² = 1078 / 88
r² = 539 / 44
r² = 12.25
r = √12.25
r = 3.5 cm

Volume of sphere = 4πr³
= 4/3 ×22/7 × 3.5 × 3.5 × 3.5
= 179.67 cm³

Answer 2

$\huge{\underline{\underline{\mathrm{\red{GIVEN:-}}}}}$

• Surface area of sphere = 154 cm²

$\huge{\underline{\underline{\mathrm{\red{NEED\:TO\:FIND:-}}}}}$

Find the Volume of Sphere = ?

$\huge{\underline{\underline{\mathrm{\red{FORMULA \:USED:-}}}}}$

$\large{\boxed{\bf{\blue{Volume \: of \: sphere = \frac{4}{3}π{r}^{3}}}}}$

$\large{\boxed{\bf{\blue{Surface\:area \: of \: sphere = 4π{r}^{2}}}}}$

$\huge{\underline{\underline{\mathrm{\red{SOLUTION:-}}}}}$

We have given that, surface area of sphere is 154 cm², we need to find the radius of the sphere

Putting the given values in the formula, we get

$\implies$$\bf{154 = 4\times\frac{22}{7}\times{r}^{2}}$

$\implies$$\bf{154 = \frac {88}{7}\times{r}^{2}}$

$\implies$$\bf{ {r}^{2} =\large \frac{154\times7}{88}}$

$\implies$ $\cancel\dfrac{1078}{88}$

$\implies$$\bf{r= \sqrt{\frac{49}{4}}}$

$\implies$$\large\bf\green{r = \frac{7}{2}}$

Now, we have to find the Volume of Sphere

Putting the values in formula, we get

$\implies$$\large\bf{Volume = \frac{4}{3}\timesπ{r}^{3}}$

$\implies$$\bf{Volume = \frac{4}{3}\times\frac{22}{7}\times\frac{7}{2}\times\frac{7}{2}\frac{7}{2}}$

$\implies$$\bf{Volume =\large \frac{30184}{168}}$

$\implies$$\bf{Volume = }$$\cancel\dfrac{30184}{168}$

$\implies$$\large\bf\green{Volume = 179.66\:{cm}^{3}}$

Thus, the Volume of sphere is 179.66 cm³

$\large{\underline{\underline{\mathrm{\red{FINAL\:ANSWER:-}}}}}$

$\huge{\boxed{\boxed{\mathrm{\green{Volume = 179.66\:{cm}^{3}}}}}}$