Question

If the radius of a balloon is doubled by pumping air into it, find the ratio of the two surface area .

Answer 1

Answer:

1:2

Step-by-step explanation:1:2

Answer 2

The required ratio of the two surface area is $\frac{S_1}{S_2}=\frac{1}{4}$.

Step-by-step explanation:

Consider the provided information.

Let the radius of a balloon is $r_1$

The surface area of the balloon is: $S_1=4\pi r_1^2$

After pumping air the new radius of the ballon is $r_2$

The radius of a balloon is doubled by pumping air into it,

$r_2=2r_1$

The surface area of the new balloon is:

$S_2=4\pi r_2^2$

Substitute $r_2=2r_1$ in $S_2=4\pi r_2^2$

$S_2=4\pi (2r_1)^2$

$S_2=16\pi r_1^2$

Now find the ratio of the two surface are:

$\frac{S_1}{S_2}=\frac{4\pi r_1^2}{16\pi r_1^2}$

$\frac{S_1}{S_2}=\frac{1}{4}$

Hence, the required ratio of the two surface area is $\frac{S_1}{S_2}=\frac{1}{4}$.

#Learn more

The surface area of a ball is 1386 cm2. Find the radius of ball.

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