Question

if the radius of the sphere is increased by 100% the volume of the corresponding sphere is increased by... ​

Answer 1

If d radius of d sphere is increased by 100% thn d volume of d corresponding sphere is increased by.. 700%

Let the initial radius of the sphere be “r₁” and the initial volume be “V₁”.

So, the Initial Volume of the sphere, V₁ = 3/4 * πr₁³ …… (i)

It is given that, the radius of sphere is increased by 100% i.e.,

The new radius, r₂ = r₁ + (100% of r₁) = 2r₁

Now,

The New Volume of the sphere,

V₂ = 3/4 * πr₂³

⇒ V₂ = 3/4* π * (2r₁)³

⇒ V₂ = 3/4 * π * 8 * r₁³

⇒ V₂ = 8 * V₁ ……. [substituting from (i)]

Thus,

The volume of the corresponding sphere is increased by,

= [(V₂ – V₁)/V₁] * 100

= [(8V1 – V₁)/V₁] * 100

= [7V₁/V₁] * 100

= 7 * 100

= 700%

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