Let the initial radius of sphere be r₁ and volume V₁ and final radius be r₂ and volume V₂.
Volume of Sphere, V₁ = 4/3π(r₁)³
Given, Increasing the Radius of a Sphere by 10%.
Increase in Radius = 10 % of r₁
= r₁ × 10/100
= r₁/10
New radius, r₂ = r₁ + r₁ /10
r₂ = 11r₁ /10
r₂/r₁ = 11/10
r₁/r₂ = 10/11
New Volume, V₂ = 4/3π(r₂)³
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Answers & Comments
We know that,
For a sphere with radius r,
Volume of the sphere ( V) = 4/3πr³
Let's consider that, We are considering this sphere in this problem.
So, Radius of sphere is increased by 10%
New radius = r + 10% of r = 110/100r = 11/10r
New volume = 4/3 ( π)( 11/10r)³ = 1331/100 ( V )
Increase in percentage of volume = Change in volume / Initial volume * 100
= 1331/1000V - V / V * 100
= V ( 1331/1000 - 1 ) /V * 100
= ( 331/1000) * 100
= 331/10
= 33.1 %
Therefore, increase in percentage of volume is 33.1%
Let the initial radius of sphere be r₁ and volume V₁ and final radius be r₂ and volume V₂.
Volume of Sphere, V₁ = 4/3π(r₁)³
Given, Increasing the Radius of a Sphere by 10%.
Increase in Radius = 10 % of r₁
= r₁ × 10/100
= r₁/10
New radius, r₂ = r₁ + r₁ /10
r₂ = 11r₁ /10
r₂/r₁ = 11/10
r₁/r₂ = 10/11
New Volume, V₂ = 4/3π(r₂)³