Question

If the surface area of a soap bubble increases by 21%,the % increase in volume will be

Answer 1

surface area 4 pi r2

For an increase of surface area, the radius has to increase.

So, let, r_1 be initial radius and r_2 be radius after expansion.

According to the question-

$\frac{121}{100} 4\pi{r_1}^{2} = 4\pi {r_2}^2$
(121/100)(r_1)2 = (r_2)2
or, (r_2)/(r_1) = 11/10 (sqrt of both sides)

The increase in volume-

$\frac{\frac{4}{3} \pi{(r_2)}{3}}{\frac{4}{3} \pi {(r_1)}{3}}$
which comes to {(r_2)/(r_1)}3 = (11/10)3
1331/1000 = 1.33

Increase in percentage = 1.33 × 100% = 133%

Increase = (133 -100) = 33%

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