Question

The diameter of a sphere is decreased by 25% . By what percentage does its curved surface area decrease ? ​

Answer 1

$\sf\huge\bold{Answer:}$

Given :

Diameter of sphere decreased = 25%

To find :

percentage with which its curved surface area decreased

Solution :

Let D be diameter of sphere

and Radius be r = D/2

Curved surface area of sphere

$:⟶A = 4\pi \: r {}^{2} = 4\pi \frac{D}{2} = 2\pi \: D$

Since,diameter is decreased by 25%

New diameter

$\frac{100 - 25}{100} \times d \\ = \frac{75}{100} d \\ = \frac{3}{4} d$

New radius

$= \frac{3}{4 \times 2}d$

New surface area

$:⟶A = 4\pi \: r {}^{2} = 4\pi \: (\frac{3}{4 \times 2} d ){}^{2} = \frac{9}{16} \pi \: d {}^{2}$

Decrease in Surface Area

$= \pi \: d {}^{2} - \frac{9}{16} \pi \: d {}^{2} = \frac{7}{16} \pi \: d {}^{2}$

So,% decrease in surface area

$\sf = \frac{decrease \: in \: surface \: area}{surface \: area} \times 100 \%$

$= \frac{7\pi \: d {}^{2} }{16\pi \: d {}^{2} } \times 100$

$= \frac{7}{16} \times 100\%$

$= 43.75\%$

$\fbox{Percentage with which its curved surface area decreased is 43.75}$