Class 10 Maths Chapter 12 Surface Areas and Volumes – Exercise 12.2 NCERT Solutions

Introduction

Exercise 12.2 focuses on volumes of solid figures such as cubes, cuboids, cylinders, spheres, and hemispheres. These problems help you calculate the space occupied by 3‑D objects, which is essential in real‑life applications like storage, construction, and design.

Formula Used

• Cube:

$$V=a^3$$

• Cuboid:

$$V=l\cdot b\cdot h$$

• Cylinder:

$$V=\pi r^{2}h$$

• Sphere:

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

• Hemisphere:

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

NCERT Questions with Solutions (10)

Q1. Find volume of cube of side 7 cm.

$$V=a^3=7^3=343{\text{cm}}^3$$

Q2. Find volume of cuboid with dimensions 5 cm × 4 cm × 3 cm.

$$V=l\cdot b\cdot h=5\times 4\times 3=60{\text{cm}}^3$$

Q3. Find volume of cylinder with radius 7 cm and height 10 cm.

$$V=\pi r^{2}h=\frac{22}{7}\times 49\times 10=1540{\text{cm}}^3$$

Q4. Find volume of sphere with radius 7 cm.

$$V=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times 343=1437.33{\text{cm}}^3$$

Q5. Find volume of hemisphere with radius 7 cm.

$$V=\frac{2}{3}\pi r^3=\frac{2}{3}\times \frac{22}{7}\times 343=718.67{\text{cm}}^3$$

Q6. Find volume of cube of side 10 cm.

$$V=a^3={10}^3=1000{\text{cm}}^3$$

Q7. Find volume of cuboid with dimensions 12 cm × 10 cm × 5 cm.

$$V=l\cdot b\cdot h=12\times 10\times 5=600{\text{cm}}^3$$

Q8. Find volume of cylinder with radius 14 cm and height 20 cm.

$$V=\pi r^{2}h=\frac{22}{7}\times 196\times 20=12320{\text{cm}}^3$$

Q9. Find volume of sphere with radius 14 cm.

$$V=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times 2744=11494.67{\text{cm}}^3$$

Q10. Find volume of hemisphere with radius 14 cm.

$$V=\frac{2}{3}\pi r^3=\frac{2}{3}\times \frac{22}{7}\times 2744=5747.33{\text{cm}}^3$$

FAQs (10)

1. What is volume? Space occupied by solid.

2. Formula for cube volume?

$$V=a^3$$

3. Formula for cuboid volume?

$$V=l\cdot b\cdot h$$

4. Formula for cylinder volume?

$$V=\pi r^{2}h$$

5. Formula for sphere volume?

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

6. Formula for hemisphere volume?

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

7. Unit of volume? Cubic units (${\text{cm}}^3,{\text{m}}^3$).

8. Can volume be negative? No, always positive.

9. Why is volume important? Used in storage, construction, and design.

10. Why is this exercise important? It builds skills in calculating volumes of 3‑D solids.

Conclusion

Exercise 12.2 has 10 solved questions and 10 FAQs that strengthen your understanding of volumes of solid figures. This builds the foundation for advanced problems in Class 10 Maths.

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New Syllabus-Class 10 Maths Chapter 12 Surface Areas and Volumes – Exercise 12.2 NCERT Solutions