Question

The diameter of a sphere is decreased by 25 percent by what percent does it's surface are decrease

Answer 1

Let's say the the original diameter is 'd'.
Now the diameter is decreased by 25% i.e.
the new diameter dⁿ is d-25%d=(0.75)d. Formula for curved surface area S=Πd².
Let the new surface area be Sⁿ=Π(dⁿ)².
Take the ratio, Sⁿ:S=(dⁿ)²:d²= (3/4)².
New surface area is Sⁿ=(9/16)S. Decrease in surface area is S-(9/16)S=(7/16)S. Percentage decrease in surface area is 43.75.
Hence surface area decreases by 43.75%