Question

if the radius of sphere is decreased by 25%.then the % decrease in its area is​

Answer 1

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Let me try to answer this in detail.

Let D be the diameter of the sphere, and the radius of the sphere r is D2.

The curved surface area of the sphere is A=4πr2=4πD2=πD2.

Since the diameter is decreased by 25 , the new diameter is 75100×d=3d4.

New surface area =4πr2=4π(3d2⋅4)2=916πd2

Decrease in surface area =πd2−916πd2=716πd2

So the % decrease in Surface Area= DecreaseinsurfaceareaSurfacearea×100%

=7πd216πd2×100=716×100=43.75%

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Answer 2

Let D be the diameter of the sphere, and the radius of the sphere r is D2.

The curved surface area of the sphere is A=4πr2=4πD2=πD2.

Since the diameter is decreased by 25 , the new diameter is 75100×d=3d4.

New surface area =4πr2=4π(3d2⋅4)2=916πd2

Decrease in surface area =πd2−916πd2=716πd2

So the % decrease in Surface Area= DecreaseinsurfaceareaSurfacearea×100%

=7πd216πd2×100=716×100=43.75%

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