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The radius of a sphere is increased by 10%. Prove that the volume will be increased by 33.1% approximately.
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Let the radius be r.
Volume , v1=4/3πr^3
New, radius = r + r/10 =11r/10
New, volume, v2=4/3×π×11/10×11/10×11/10 ×r^3
Increase in volume =v2-v1 =4/3πr^3(1.331-1)
Increase percent = {4/3πr^3(0.331) ×100} percent /4/3πr^3
=33.1percent
Volume , v1=4/3πr^3
New, radius = r + r/10 =11r/10
New, volume, v2=4/3×π×11/10×11/10×11/10 ×r^3
Increase in volume =v2-v1 =4/3πr^3(1.331-1)
Increase percent = {4/3πr^3(0.331) ×100} percent /4/3πr^3
=33.1percent
kashishkumari868:
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