Class 9 Maths Chapter 11 Surface Areas and Volumes – Exercise 11.3 NCERT Solutions

Introduction

Exercise 11.3 focuses on volumes of spheres and hemispheres. Students learn how to apply the formula for the volume of a sphere and hemisphere to solve practical problems involving balls, globes, and containers. This exercise builds strong visualization and mensuration skills.

Key Formulas

1. Volume of Sphere:

$$V=\frac{4}{3}\pi r^3$$

2. Volume of Hemisphere:

$$V=\frac{2}{3}\pi r^3$$

Common Mistakes

• Using diameter instead of radius in formula.

• Forgetting to cube the radius.

• Confusing surface area with volume.

• Not converting units properly (cm${}^3$, m${}^3$).

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

Q1. Find volume of sphere of radius 7 cm.

$$V=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times 7^3=1437.33{\text{cm}}^3$$

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

$$V=\frac{4}{3}\pi r^3=1437.33{\text{cm}}^3$$

Q3. Find volume of sphere of radius 10.5 cm.

$$V=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times (10.5{)}^3=4851{\text{cm}}^3$$

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

$$V=4851{\text{cm}}^3$$

Q5. Find volume of sphere of radius 3.5 cm.

$$V=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times (3.5{)}^3=179.67{\text{cm}}^3$$

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

$$V=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times 216=904.32{\text{cm}}^3$$

Q7. Find volume of sphere of radius 0.7 m.

$$V=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times (0.7{)}^3=1.44{\text{m}}^3$$

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

$$V=1.44{\text{m}}^3$$

Q9. Find volume of sphere of radius 2.1 cm.

$$V=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times (2.1{)}^3=38.8{\text{cm}}^3$$

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

$$V=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times (1.75{)}^3=22.45{\text{cm}}^3$$

FAQs (10)

FAQ1. What is formula for volume of sphere? $\frac{4}{3}\pi r^3$.

FAQ2. What is formula for volume of hemisphere? $\frac{2}{3}\pi r^3$.

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

FAQ4. What is unit of volume? Cubic units (cm${}^3$, m${}^3$).

FAQ5. What is difference between surface area and volume? Surface area measures covering, volume measures capacity.

FAQ6. What is real‑life example of sphere? Ball, globe, orange.

FAQ7. Why cube radius in formula? Volume depends on three dimensions.

FAQ8. What is volume of hemisphere? Half of sphere volume.

FAQ9. Why is Exercise 11.3 important? It builds foundation for 3D mensuration.

FAQ10. What is practical use of sphere volume? Used in packaging, design, and science.

Conclusion

Exercise 11.3 covers volumes 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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