Question

TSA of solid hemisphere is 462 cm square .what is its volume

Answer 1

Answer:

$\large\bold\red{Volume = 718.67 \: {cm}^{3}}$

Step-by-step explanation:

Given,

TSA of a solid hemisphere = 462 sq.cm

But,

We know that,

TSA of solid hemisphere is given by formula,

$\large \boxed{\purple{3\pi {r}^{2} }}$

Where,

• r is the radius of hemisphere.

Therefore,

We have,

$= > 3\pi {r}^{2} = 462 \\ \\ = > {r}^{2} = \frac{462}{3\pi} \\ \\ = > {r}^{2} = \frac{ \cancel{462}}{3} \times \frac{7}{ \cancel{22}} \\ \\ = > {r}^{2} = \frac{21 \times 7}{3} \\ \\ = > {r}^{2} = \frac{3 \times 7 \times 7}{3} \\ \\ = > {r}^{2} = {7}^{2} \\ \\ = > r = 7$

Therefore,

Radius , r = 7 cm

Now,

We know that,

Volume of hemisphere is given by formula,

$\large \boxed{ \purple{\frac{2}{3} \pi {r}^{3} }}$

Therefore,

We get,

$= > v = \frac{2}{3} \times \frac{22}{7} \times {7}^{3} \\ \\ = v = 44 \times \frac{49}{3} \\ \\ = > v = \frac{2156}{3} \\ \\ = > \large \boxed{ \bold{ v = 718.67 \: {cm}^{3} }}$

Answer 2

Given :-----

• Total surface Area of solid Hemisphere = 462cm²

To Find :----

• Volume of Hemisphere ?

Formula To be used :------

• TSA of Hemisphere = 3πr²
• Volume of Hemisphere = 2/3πr³
• π = 22/7

it is given that is TSA is 462cm².

so,

Equating it with the above formula we get,

$3\pi {r}^{2} = 462 \\ \\ {r}^{2} = \frac{462 \times 7}{3 \times 22} \\ \\ {r}^{2} = 49 \\ \\ r = 7 \: cm$

Now, putting value of r in volume formula we get,

$v = \frac{2}{3} \pi \: {r}^{3} \\ \\ v = \frac{2}{3} \times \frac{22}{7} \times {7}^{3} \\ \\ v = \frac{44 \times 49}{3} \\ \\ v = 718.67 \: cm^{3}$

Hence Volume of Hemisphere will be = 718.67cm³

______________________________

Extra Brainly knowledge :----

1) CSA of Hemisphere = 2πr²

2) TSA of sphere = 4πr²

3) Volume of sphere = 4/3 πr³ ..