Class 10 Maths Chapter 12 Surface Areas and Volumes – Exercise 12.1 NCERT Solutions

Introduction

Exercise 12.1 focuses on surface areas of solid figures such as cubes, cuboids, spheres, hemispheres, and right circular cylinders. These problems help you calculate the total surface area (TSA) and curved surface area (CSA) of 3‑D objects, which is essential in real‑life applications like packaging, construction, and design.

Formula Used

• Cube (side $a$):

$$\text{TSA}=6a^2,V=a^3$$

• Cuboid (length $l$, breadth $b$, height $h$):

$$\text{TSA}=2(lb+bh+hl),V=l\cdot b\cdot h$$

• Cylinder (radius $r$, height $h$):

$$\text{CSA}=2\pi rh,\text{TSA}=2\pi r(h+r),V=\pi r^{2}h$$

• Sphere (radius $r$):

$$\text{Surface Area}=4\pi r^2,V=\frac{4}{3}\pi r^3$$

• Hemisphere (radius $r$):

$$\text{CSA}=2\pi r^2,\text{TSA}=3\pi r^2,V=\frac{2}{3}\pi r^3$$

NCERT Questions with Solutions (10)

Q1. Find TSA of cube of side 7 cm.

$$\text{TSA}=6a^2=6\times 7^2=294{\text{cm}}^2$$

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

$$\text{TSA}=2(lb+bh+hl)=2(20+12+15)=94{\text{cm}}^2$$

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

$$\text{CSA}=2\pi rh=2\times \frac{22}{7}\times 7\times 10=440{\text{cm}}^2$$

Q4. Find TSA of cylinder with radius 7 cm and height 10 cm.

$$\text{TSA}=2\pi r(h+r)=2\times \frac{22}{7}\times 7\times (10+7)=748{\text{cm}}^2$$

Q5. Find surface area of sphere with radius 7 cm.

$$\text{Surface Area}=4\pi r^2=4\times \frac{22}{7}\times 49=616{\text{cm}}^2$$

Q6. Find CSA of hemisphere with radius 7 cm.

$$\text{CSA}=2\pi r^2=2\times \frac{22}{7}\times 49=308{\text{cm}}^2$$

Q7. Find TSA of hemisphere with radius 7 cm.

$$\text{TSA}=3\pi r^2=3\times \frac{22}{7}\times 49=462{\text{cm}}^2$$

Q8. Find TSA of cube of side 10 cm.

$$\text{TSA}=6a^2=6\times {10}^2=600{\text{cm}}^2$$

Q9. Find TSA of cuboid with dimensions 12 cm × 10 cm × 5 cm.

$$\text{TSA}=2(lb+bh+hl)=2(120+50+60)=460{\text{cm}}^2$$

Q10. Find surface area of sphere with radius 14 cm.

$$\text{Surface Area}=4\pi r^2=4\times \frac{22}{7}\times 196=2464{\text{cm}}^2$$

FAQs (10)

1. What is TSA? Total Surface Area = sum of all outer surfaces.

2. What is CSA? Curved Surface Area = curved portion only.

3. What is volume? Space occupied by solid.

4. Formula for cube TSA?

$$\text{TSA}=6a^2$$

5. Formula for cuboid TSA?

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

6. Formula for cylinder CSA?

$$\text{CSA}=2\pi rh$$

7. Formula for sphere surface area?

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

8. Formula for hemisphere TSA?

$$\text{TSA}=3\pi r^2$$

9. Why is surface area important? Used in packaging, painting, and design.

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

Conclusion

Exercise 12.1 has 10 solved questions and 10 FAQs that strengthen your understanding of surface areas 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 12.1 NCERT Solutions