The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

Question

cdquestions Admin · Accepted Answer

Radius (r 1 ) of spherical balloon = 7 cm  Radius (r 2 ) of spherical balloon, when air is pumped into it = 14 cm $\text{Required ratio}=\frac{\text{Initial surface area}}{\text{Surface area after pumping air into the balloon}}$ $=\frac{4\pi r^2_1}{4\pi r^2_2}$ $=(\frac{r_1}{r_2})^2$ $=(\frac{7}{14})^2=\frac{1}{4}$ Therefore, the ratio between the surface areas in these two cases is 1:4.

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

Solution and Explanation

Top CBSE Class IX Mathematics Questions

Top CBSE Class IX Questions