Question

Curved surface area of a hemisphere is 905 1/7cm3 , what is its volume?

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Answer 1

Given :-

• Curved Surface Area of the Hemisphere = 905 (1/7)cm².

To Find :-

• Volume of the hemisphere.

Solution :-

• C.S.A of hemisphere = 905(1/7) = 905×7+1/7 = 6336/7 cm² .

As we know that,

C.S.A. of the Hemisphere = 2π r²

6336/7 = 2πr²

⇒ 6336/7 = 2(22/7) + r²

⇒ r² = 6336/7 × 7/44

⇒ r = √6336/44

⇒ r = 12cm.

Volume of the Hemisphere = ⅔ π r³

⇒ 2/3 × 22/7 × (12)³

⇒3620.57 cm³.

Thus, the volume of the Hemisphere is 3620.57cm³.

Answer 2

Correct question:

The Curved Surface Area of a hemisphere is $905\frac{1}{7}$ cm², what is its volume?

SOLUTION:

$905 \frac{1}{7} = 7 \times 905 + 1 = \frac{6336}{7} cm^{2}$

$\boxed{\red{\sf{Formula\ for\ CSA\ of\ hemisphere-}}}$

$= 2\pi r ^{2}\ unit^{2}\ [\therefore \rm{In\ which\ 'r'\ is\ the\ 'radius'\ of\ the\ hemisphere}]$

So, we can find the radius of the hemisphere with the help of the CSA.

$\implies 2 \pi r^{2} = \frac{6336}{7}$

$\implies 2 \times \frac{22}{7} \times r^{2} = \frac{6336}{7}$

$\implies \frac{44}{7} \times r^{2} = \frac{6336}{7}$

$\implies r^{2} = \frac{6336}{\not{7}} \times \frac{\not{7}}{44}$

[Taking 44/7 to RHS]

$\implies r^{2} = \frac{6336}{44}$

$\implies r^{2} =144$

$\implies r = \sqrt{144}$

$\therefore \boxed{\red{\rm{r = 12cm}}}$

Now, we got the value of 'r' = radius fo the hemisphere is 12cm.

We have to find the volume.

$\boxed{\bf{Fomula-}}$

$\boxed{\blue{\frac{2}{3} \pi r^{2}\ unit\ cube}}$

$= \frac{2}{3} \times \frac{22}{7} \times (12) \times (12) \times (12)$ cm cube.

$= 2 \times \frac{22}{7} \times (\bf{4}) \times (12) \times (12)$ cm cube.

$= \frac{25344}{7}$ cm cube

$\boxed{\rm{ =3620.57\ cm\ cube}}$

Hence,

The volume of the hemisphere is 3620.57 cm cube.