Welcome 2016! Part 15

Let's take the diameter of sphere to be $d$ .

So its curved surface area is $\pi d^2$ .

The new diameter is $\frac{3}{4}d$ .

Now the curved surface area is $\frac{9}{16}\pi d^2$ .

$\% \text{ Decrease}=\frac{\left(1-\frac{9}{16}\right)\pi d^2}{\pi d^2}×100=\frac{7}{16}×100=\boxed{43.75}$

.75^2=.5625
1.00-.5625=.4375=43.75%

Let $d$ be the diameter of the original sphere, then the diameter of the new sphere is $0.75d$ . The formula for the surface area of a sphere in terms of its diameter is $\pi d^2$ . So the surface area of the original sphere is $\pi d^2$ and the new sphere is $\pi (0.75d)^2=0.5625\pi d^2$ . The percentage decreased in its surface area is $(1-0.5625)(100\%)=\boxed{43.75\%}$

$\frac{S1}{S2}$ $=$ $\frac{d^2}{(0.75d)^2}$

$\frac{S1}{S2}$ $=$ $\frac{1}{0.5625}$

$S2$ $=$ $0.5625$ $S1$

$1-0.5625=0.4375$ $*$ $100$ % $=$ $43.75$ %