Surface Areas & Volumes | Exercise 13.4 | Q4

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.

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

Exercise 13.1 | Surface Area of Cubes & Cuboids

1. Class 9 Exercise 13.1 Question 3 | Height of hall ▶
2. Class 9 Exercise 13.1 Question 6 | TSA of Herbarium ▶
3. Class 9 Exercise 13.1 Question 7 | Shanti Sweets ▶

Exercise 13.2 | Surface Area of Cylinders

1. Class 9 Exercise 13.2 Question 3 | CSA TSA of Metal Pipe ▶
2. Class 9 Exercise 13.2 Question 4 | Roller & Playground ▶
3. Class 9 Exercise 13.2 Question 9 | Cylindrical Petrol Tank ▶
4. Class 9 Exercise 13.2 Question 10 | CSA of Decorative Lampshade ▶

Exercise 13.3 | Surface Area of Cones

1. Class 9 Exercise 13.3 Question 5 | Length of Tarpaulin 3 m wide ▶
2. Class 9 Exercise 13.3 Question 8 | Cost of painting conical barricades ▶

Exercise 13.4 | Surface Area of Spheres & Hemispheres

1. Class 9 Exercise 13.4 Question 8 | Outer CSA of hemispherical bowl ▶
2. Class 9 Exercise 13.4 Question 9 | Surface area of sphere & Cylinder ▶