Question

The curved surface area of a hemisphere is

157 cm square

, what is its

radius?

(π = 3.14)​

Answer 1

Answer:

Answer is quite mad. XD

But 100% sure that it is correct.

Step-by-step explanation:

Curved surface area of a hemisphere

$= 2\pi {r}^{2}$

From the given condition,

$157 = 2 \times \frac{22}{7} \times {r}^{2}$

${r}^{2} = \frac{157 \times 7}{2 \times 22}$

$r = \sqrt{ \frac{1099}{44} }$

Answer 2

$\Large {\underline { \sf \orange{Clarification :}}}$

Here, as per the provided question we are given that the C.S.A of hemisphere is 157 cm².We have to find its radius. According to the question, we have to take the value of π as 3.14.

We'll use the formula of the C.S.A of hemisphere in order to form a linear equation and then we'll solve the equation and find the radius using transposition method.

$\bf \red { \dag }$ Transposition method :

• This is the method used to solve a linear equation having variables and constants.
• In this method, we transpose the values from R.H.S to L.H.S and vice-versa and changes its sign while transposing to find the value of the unknown value.

$\Large {\underline { \sf \orange{Explication \: of \: Steps :}}}$

★ C.S.A of hemisphere = 2πr²

• r = radius

Substituting values,

→ 157 = 2 × 3.14 × r²

→ 157 = 6.28 × r²

→ $\sf {\dfrac{157}{6.28} }$ = r²

→ $\sf {\dfrac{157 \times 100}{628} }$ = r²

→ $\cancel{\sf {\dfrac{15700}{628} }}$ = r²

→ 25 = r²

→ √25 = r

→ 5 = r

$\longrightarrow$ ❝ $\boxed{ \sf \orange { 5 \: cm = Radius }}$ ❞

❝ Therefore, radius of the hemisphere is $\pmb { \mathfrak \gray { 5 \: cm }}$.❞

$\Large {\underline { \sf \orange{A \: Little \: Further. . . .!}}}$

More formulae related to hemisphere and sphere :

⑴ Surface area of a sphere = 4πr²

⑵ Volume of a sphere = $\sf { \dfrac{4}{3}\pi {r}^{3}}$

⑶ Volume of empty sphere = 4π($\sf {{R}^{3}- {r}^{3}}$)

⑷ T.S.A of hemisphere = 3πr²

⑸ Volume of hemisphere = $\sf { \dfrac{2}{3}\pi {r}^{3}}$