Class 9 Maths Chapter 11 Surface Areas and Volumes – Exercise 11.1 NCERT Solutions

Introduction

Exercise 11.1 introduces the surface area of solid figures. You’ll learn how to calculate the surface area of cubes, cuboids, cylinders, cones, and spheres using their respective formulas.

Key Formulas

• Cuboid:

$$\text{Surface Area}=2(lb+bh+hl)$$

• Cube:

$$\text{Surface Area}=6a^2$$

• Cylinder:

$$\text{Surface Area}=2\pi r(h+r)$$

• Cone:

$$\text{Surface Area}=\pi r(l+r)$$

• Sphere:

$$\text{Surface Area}=4\pi r^2$$

Solved Questions (Step by Step)

Q1. Find the surface area of a cube of side 7 cm.

Solution:

$$\text{Surface Area}=6a^2=6\cdot 7^2=6\cdot 49=294{\text{cm}}^2$$

Q2. Find the surface area of a cuboid of dimensions 5 cm × 4 cm × 3 cm.

Solution:

$$\text{Surface Area}=2(lb+bh+hl)=2(5\cdot 4+4\cdot 3+3\cdot 5)=2(20+12+15)=94{\text{cm}}^2$$

Q3. Find the surface area of a sphere of radius 7 cm.

Solution:

$$\text{Surface Area}=4\pi r^2=4\cdot \pi \cdot 7^2=4\cdot \pi \cdot 49=616{\text{cm}}^2$$

Q4. Find the surface area of a cylinder of radius 5 cm and height 10 cm.

Solution:

$$\text{Surface Area}=2\pi r(h+r)=2\pi \cdot 5(10+5)=2\pi \cdot 75=471{\text{cm}}^2$$

Q5. Find the surface area of a cone of radius 3 cm and slant height 5 cm.

Solution:

$$\text{Surface Area}=\pi r(l+r)=\pi \cdot 3(5+3)=\pi \cdot 24=75.4{\text{cm}}^2$$

FAQs (10 for Exercise 11.1)

1. Q: What is surface area? A: The total area of all outer surfaces of a solid figure.

2. Q: What is the surface area of a cube? A: $6a^2$, where $a$ is the side length.

3. Q: What is the surface area of a cuboid? A: $2(lb+bh+hl)$.

4. Q: What is the surface area of a cylinder? A: $2\pi r(h+r)$.

5. Q: What is the surface area of a cone? A: $\pi r(l+r)$.

6. Q: What is the surface area of a sphere? A: $4\pi r^2$.

7. Q: Why is surface area important? A: It helps in calculating paint, wrapping, or covering materials.

8. Q: What is the difference between surface area and volume? A: Surface area measures covering space; volume measures occupied space.

9. Q: What is the unit of surface area? A: Square units (cm², m², etc.).

10. Q: Can surface area be calculated without formulas? A: Not accurately; formulas are essential.

Conclusion

Exercise 11.1 has 15 questions that strengthen your understanding of surface area calculations for solid figures. This builds the foundation for solving real‑life problems involving packaging, painting, and construction.

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New Syylabus-Class 9 Maths Chapter 11 Surface Areas and Volumes – Exercise 11.1 NCERT Solutions