Math, asked by SanjyotBhujbal6893, 11 months ago

The radius of a spherical balloon increases from 14 cm to 21 cm as air is pumped into it. Find the ratio of the surface areas of the balloon in the two situations.

Answers

Answered by hukam0685
5

Answer:

Ratio of the surface areas of the balloon in the two situations 4:9

Step-by-step explanation:

Surface area of sphere( Balloon)

 = 4\pi {r}^{2}  \:  {cm}^{2}  \\  \\

Surface area of sphere when radius is 14 cm

 S_1= 4 \times  \frac{22}{7}  \times ( {14)}^{2}  \\  \\  = 4 \times  \frac{22}{7}   \times 196 \\  \\  = 88 \times 28 \\  \\ S_1 = 2464 \:  {cm}^{2}  \\

Surface area of sphere when radius increases to 21 cm

S_2= 4 \times  \frac{22}{7}  \times ( {21)}^{2}  \\  \\  = 4 \times  \frac{22}{7}   \times 441 \\  \\  = 88 \times 63 \\  \\S_2  = 5544 \:  {cm}^{2}  \\  \\

Ratio of surface area in both the situation

 \frac{S_1}{S_2}  =  \frac{88 \times 28}{88 \times 63}  \\  \\ \frac{S_1}{S_2}  =  \frac{</strong><strong>4</strong><strong>}{</strong><strong>9</strong><strong>}  \\  \\

Hope it helps you

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