Question

The radius of sphere is increased by 15 %.The resultant change in surface are

Answer 1

Answer:

32.25% (or 30% approximately)

Step-by-step explanation:

Surface area = 4πr²

From above

Area is proportional to r²

So,

A2/A1 = (r2/r1)²

(A2/A1) - 1 = (r2/r1)² - 1

(A2 - A1)/A1 = (r2/r1)² - 1

A2 - A1 = A1 × [(r2/r1)² - 1]

∆A = A1 × [(r2/r1)² - 1]

∆A = 100% × [(115%/100%)² - 1]

= 100% × [1.15² - 1]

= 100% × [1.3225 - 1]

= 100% × 0.3225

= 32.25%