Class 9 Maths Chapter 11 Surface Areas and Volumes – Exercise 11.2 NCERT Solutions

Introduction

Exercise 11.2 focuses on surface areas of a sphere. Students learn how to apply the formula for the curved surface area of a sphere and solve practical problems involving globes, balls, and hemispheres. This exercise strengthens spatial visualization and problem‑solving skills.

Key Formulas

1. Surface Area of Sphere:

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

2. Surface Area of Hemisphere:

   • Curved surface area:

$$2\pi r^2$$

• Total surface area:

$$3\pi r^2$$

Common Mistakes

• Confusing curved surface area with total surface area.

• Forgetting to square the radius.

• Using diameter instead of radius in formula.

• Not applying $\pi =\frac{22}{7}$ or 3.14 consistently.

NCERT Questions with Step‑by‑Step Solutions (10)

Q1. Find surface area of sphere of radius 7 cm.

$$\text{Surface Area}=4\pi r^2=4\times \frac{22}{7}\times 7^2=616{\text{cm}}^2$$

Q2. Find surface area of sphere of diameter 14 cm. Radius $r=7$.

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

Q3. Find surface area of sphere of radius 10.5 cm.

$$\text{Surface Area}=4\pi r^2=4\times \frac{22}{7}\times (10.5{)}^2=1386{\text{cm}}^2$$

Q4. Find surface area of sphere of diameter 21 cm. Radius $r=10.5$.

$$\text{Surface Area}=4\pi r^2=1386{\text{cm}}^2$$

Q5. Find surface area of sphere of radius 3.5 cm.

$$\text{Surface Area}=4\pi r^2=4\times \frac{22}{7}\times (3.5{)}^2=154{\text{cm}}^2$$

Q6. Find surface area of sphere of diameter 12 cm. Radius $r=6$.

$$\text{Surface Area}=4\pi r^2=4\times \frac{22}{7}\times 36=452.57{\text{cm}}^2$$

Q7. Find surface area of sphere of radius 0.7 m.

$$\text{Surface Area}=4\pi r^2=4\times \frac{22}{7}\times (0.7{)}^2=6.16{\text{m}}^2$$

Q8. Find surface area of sphere of diameter 1.4 m. Radius $r=0.7$.

$$\text{Surface Area}=6.16{\text{m}}^2$$

Q9. Find surface area of sphere of radius 2.1 cm.

$$\text{Surface Area}=4\pi r^2=4\times \frac{22}{7}\times (2.1{)}^2=55.44{\text{cm}}^2$$

Q10. Find surface area of sphere of diameter 3.5 cm. Radius $r=1.75$.

$$\text{Surface Area}=4\pi r^2=4\times \frac{22}{7}\times (1.75{)}^2=38.5{\text{cm}}^2$$

FAQs (10)

FAQ1. What is formula for surface area of sphere? $4\pi r^2$.

FAQ2. What is difference between curved and total surface area of hemisphere? Curved = $2\pi r^2$, Total = $3\pi r^2$.

FAQ3. Why use radius instead of diameter? Formula requires radius; diameter must be halved.

FAQ4. What is value of $\pi$? $\pi =\frac{22}{7}$ or 3.14.

FAQ5. What is unit of surface area? Square units (cm${}^2$, m${}^2$).

FAQ6. Can spheres have curved edges? No, sphere is perfectly round.

FAQ7. What is real‑life example of sphere? Ball, globe, soap bubble.

FAQ8. Why square radius in formula? Area depends on square of radius.

FAQ9. What is surface area of hemisphere? Curved = $2\pi r^2$, Total = $3\pi r^2$.

FAQ10. Why is Exercise 11.2 important? It builds foundation for 3D geometry and mensuration.

Conclusion

Exercise 11.2 covers surface areas of spheres and hemispheres with solved examples and FAQs. Mastering these problems helps students in geometry, mensuration, and real‑life applications.

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