Question

A metal sphere of radius 20 cm is melted and then cast into small hemispheres each of radius
5 cm. Find the number of hemispheres thus
obtained.
Pls answer fast ​

Answer 1

Given,

A metal sphere of radius 20 cm is melted and then cast into small hemispheres each of radius  5 cm.

To find :

Find the number of hemispheres thus  obtained.

Solution :

Radius of sphere = 20 cm

Radius of small hemisphere = 5 cm

Now, let the number of small hemispheres obtained be 'n'

Now we know,

Volume of sphere = 4/3 πr³

Volume of hemisphere = 2/3 πr³

Now atq,

⇒ Volume of sphere = n * Volume of hemispheres

⇒ 4/3 π(20)³ = n * 2/3 π(5)³

⇒ 4/3 π * 8000 = n * 2/3 π * 125

⇒ 2 * 8000 = n * 125

⇒ 16000 = 125n

⇒ n = 16000/125

⇒ n = 128

∴ Number of hemispheres obtained = 128.

Answer 2

$\huge{\boxed{\rm{Question}}}$

A metal sphere of radius 20 cm is melted and then cast into small hemispheres each of radius 5 cm. Find the number of hemispheres thus obtained.

$\huge{\boxed{\rm{Answer}}}$

$\large{\boxed{\boxed{\sf{Given \: that}}}}$

• A metal sphere of radius 20 cm is melted and then cast into small hemispheres each of radius 5 cm.

$\large{\boxed{\boxed{\sf{To \: find}}}}$

• The number of hemispheres thus obtained.

$\large{\boxed{\boxed{\sf{Solution}}}}$

• The number of hemispheres thus obtained = 128

$\large{\boxed{\boxed{\sf{Assumption}}}}$

• Let, the number of small hemispheres obtained be ❛x❜

$\large{\boxed{\boxed{\sf{Using \: formulas}}}}$

• Volume of hemisphere = 2/3 πr³

• Volume of sphere = 4/3 πr³.

$\large{\boxed{\boxed{\sf{These \: also \: means}}}}$

• Radius means r.

• π means pi.

• Value of 22/7.

• ³ means cube.

$\large{\boxed{\boxed{\sf{What \: does \: the \: question \: says}}}}$

$\large{\boxed{\boxed{\sf{Let's \: understand \: the \: concept \: 1st}}}}$

• This question says that a metal sphere of radius 20 cm is melted and then cast into small hemispheres each of radius 5 cm. Afterthat it asks us to find the number of hemispheres thus obtained.

$\large{\boxed{\boxed{\sf{How \: to \: solve \: this \: question}}}}$

$\large{\boxed{\boxed{\sf{Let's \: see \: the \: procedure \: now}}}}$

• To solve this question we have to use given formulas to find volume of sphere and hemisphere. And we already know these formulas. Now according to the question using the formula Volume of sphere = x × Volume of hemispheres we have to put the values afterthat we get our result and it's our final result. Hence, 128 are the total number of hemispheres.

$\large{\boxed{\boxed{\sf{Full \: solution}}}}$

✞ According to the question we already know that what is given and what to find let's see it again to understand properly !

• Sphere's radius = 20 cm ( Given )

• Small hemisphere's radius = 5 cm ( Given )

• Number of hemispheres ( To find )

• Let, the number of small hemispheres obtained be ❛x❜

✞ Now, using formulas

• Volume of hemisphere = 2/3 πr³

• Volume of sphere = 4/3 πr³.

✞ Now according to the question,

• Volume of sphere = x × Volume of hemispheres.

✞ Putting the values we get the following results,

☛ Volume of sphere = x × Volume of hemispheres.

☛ 4/3 π (20)³ = x × 2/3π × 125

( Cancelling the values and π's we get the following results )

☛ 2 × 8000 = x × 125

☛16000 = 125x

☛ x = 16000 / 125

☛ x = 128

$\bold{\green{\fbox{\green{Hemispheres = 128}}}}$

Hence, 128 are the total number of hemispheres.