Question

the radius of a sphere is increased by 25% . find percentage increase in surface area

Answer 1

hope it hlps u......

Answer 2

Answer:

56.25 %

Step-by-step explanation:

Let the radius of the sphere = r,

Thus, the surface area of the sphere,

$A_1=4\pi(r)^2$

After increasing 25 %,

New radius of the circle = 125% of the radius

$=\frac{125r}{100}$

= 1.25r

Thus, the new surface area of the sphere,

$A_2=4\pi(1.25r)^2=4\pi(1.5625r^2)=6.25\pi r^2$

Hence, the percentage increase in the surface area

$=\frac{A_2-A_1}{A_1}\times 100$

$=\frac{6.25\pi r-4\pi r^2}{4\pi r^2}\times 100$

$=\frac{2.25}{4}\times 100$

$=\frac{225}{4}$

$=56.25\%$