Question

The diameter of a sphere is decreased by 25percent what percent its surface area decrease

Answer 1

Answer:

Step-by-step explanation:

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 is75100×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%