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
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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
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Verified answer
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.