Surface Areas & Volumes | Exercise 13.4 | Q4

Class 9 Maths | NCERT Solution to Exercise | Surface Area of Sphere

Question 4: 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.


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Explanatory Answer | Exrecise 13.4 Question 4

Step 1: Compute Surface Area of Balloon Before Filling Air

Radius of the spherical balloon initially, r1 = 7 cm
Surface area of the balloon initially = 4 × π × r12
= 4 × π × 72
= 4 × π × 49

Step 2: Compute Surface Area of Balloon After Filling Air

Radius of the spherical balloon after air is pumped, r2 = 14 cm
Surface area of the balloon after air is pumped = 4 × π × r22
= 4 × π × 142
= 4 × π × 196

Step 3: Compute Ratio Before & After Filling Air

Ratio of the two scenarios = \\frac{\text{Surface area of the balloon before air is pumped}}{\text{Surface area of the balloon after air is pumped}})
= \\frac{4 × π × 49}{4 × π × 196})
= \\frac{1}{4})
Ratio of surface areas of the balloon in the two scenarios = 1 : 4

 


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