📊 Class 10 Maths Chapter 16: Surface Areas and Volumes – Notes & Blog Post

 

🧮 Introduction

In this chapter, we study surface area and volume of 3D shapes such as:

• Cube

• Cuboid

• Sphere

• Hemisphere

• Cylinder

• Cone

• Frustum of Cone

It helps us calculate space occupied or area covered by these solids in real-life scenarios like tanks, pipes, ice cream cones, and more.

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📐 1. Surface Area & Volume Formulas

🧠 Where:

• $a$: edge of cube

• $r$: radius

• $h$: height

• $l$: slant height (cone/cylinder)

• $r_1, r_2$: radii of frustum ends

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📏 2. Conversions

• 1 cm = 0.01 m

• 1 m³ = 1000 liters

• Surface area is measured in cm², m²

• Volume is measured in cm³, m³ or liters

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🧠 3. Tips to Remember

• For hollow shapes, subtract inner volume from outer volume.

• For composite solids, calculate each part separately and then add/subtract accordingly.

• Use π = 3.14 or 22/7 as required.

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🎯 4. Real-Life Applications

• Water tanks, containers, packaging

• Conical tents, ice cream cones

• Cylindrical pipes, gas cylinders

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✍️ 5. Example Problems

Q1. A cylinder has radius 7 cm and height 10 cm. Find its total surface area.

$$\text{TSA} = 2\pi r(h + r) = 2 \times \frac{22}{7} \times 7 (10 + 7) = 2 \times 22 \times 17 = 748 \text{ cm}^2$$

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Q2. A cone has radius 3.5 cm and slant height 10 cm. Find its curved surface area.

$$\text{CSA} = \pi r l = \frac{22}{7} \times 3.5 \times 10 = 110 \text{ cm}^2$$

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✅ Key Takeaways

• Always understand shape and formula before applying.

• Use correct units: cm², m², cm³, liters, etc.

• Practice composite solids questions for higher-level exams.

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📌 Summary Table

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