Question

if T.S.A of hemisphere is 462 Sq cm. find its radius​

Answer 1

$\textbf{\huge{\red{Answer:}}}$

✔TSA of hemisphere = 3πr^2
➡462 = 3 * 22/7 * r^2
➡462 * 7/ 3 * 22 = r^2
➡49 = r^2
➡(7)^2 = r^2
➡7cm = r


$\mathbb{\huge{\red{Radius:}}}$ 7cm

Answer 2

${\boxed{\sf{TSA \ of \ hemisphere = 3 \pi r^2}}}$


$\sf{Also,}$


$\sf{TSA \ of \ hemisphere = 462 \ cm^2 \quad (Given)}$


$\therefore$


$\sf{3 \pi r^2 = 462}$


$\sf{(Taking \ \pi = {\dfrac{22}{7}} )}$


$\sf{3 × {\dfrac{22}{7}} × r^2 = 462}$


$\sf{r^2 = {\dfrac{462 × 7}{22 × 3}}}$


$\sf{r^2 = 49}$


$\sf{r = {\sqrt{49}}}$


$\sf{r = {\sqrt{(7)^2}}}$


$\sf{Removing \ the \ square \ root.}$


$\sf{r = {(7^2)}^{ {\frac{1}{2}} }}$


${\boxed{\sf{(a^m)^n = {a}^{mn}}}}$


$\sf{r = {(7)}^{2 × {\frac{1}{2}} }}$


$\sf{r = {(7)}^{ {\cancel{2}} × {\frac{1}{ {\cancel{2}} }}}}$


$\sf{r = 7 \ cm}$


$\sf\red{Hence, \ the \ radius \ is \ 7 \ cm.}$