🟣 Class 10 Maths Chapter 13: Surface Areas and Volumes – Notes & Blog Post

 

📘 Introduction

This chapter helps you calculate the surface area and volume of 3D shapes like:

• Cubes & cuboids

• Cylinders

• Cones

• Spheres & hemispheres

• Frustums (truncated cones)

You'll also learn how to apply these concepts to solve real-life problems, such as water tank capacity, metal used in a hollow pipe, or paint needed for walls.

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🔲 1. Surface Area of 3D Shapes

📦 Cube and Cuboid

• Surface Area of Cuboid = $2(lb + bh + hl)$

• Surface Area of Cube = $6a^2$

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🔵 Cylinder

• Curved Surface Area (CSA) = $2\pi rh$

• Total Surface Area (TSA) = $2\pi r(h + r)$

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🔺 Cone

• Slant Height (l) = $\sqrt{r^2 + h^2}$

• CSA = $\pi rl$

• TSA = $\pi r(l + r)$

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⚪ Sphere & Hemisphere

• Sphere:

  • CSA = $4\pi r^2$

  • TSA = $4\pi r^2$

• Hemisphere:

  • CSA = $2\pi r^2$

  • TSA = $3\pi r^2$

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🧩 Frustum of a Cone

Formed by cutting a cone parallel to its base.

• CSA = $\pi (r_1 + r_2)l$

• TSA = $\pi (r_1 + r_2)l + \pi r_1^2 + \pi r_2^2$

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🧮 2. Volume of 3D Shapes

🧊 Cube & Cuboid

• Volume of Cuboid = $l \times b \times h$

• Volume of Cube = $a^3$

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🧱 Cylinder

• Volume = $\pi r^2 h$

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⛰️ Cone

• Volume = $\frac{1}{3} \pi r^2 h$

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⚫ Sphere & Hemisphere

• Sphere Volume = $\frac{4}{3} \pi r^3$

• Hemisphere Volume = $\frac{2}{3} \pi r^3$

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🍶 Frustum

• Volume = $\frac{1}{3} \pi h (r_1^2 + r_2^2 + r_1 r_2)$

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🔍 3. Applications in Daily Life

• Calculating water capacity of tanks

• Volume of gas cylinders

• Area to be painted on walls

• Designing cones, pipes, domes

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📝 Important Formulas at a Glance

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💡 Sample Questions

Q1. Find the CSA and Volume of a cylinder of radius 7 cm and height 10 cm.

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

• Volume = $\frac{22}{7} \times 7^2 \times 10 = 1540 \text{ cm}^3$

Q2. A cone has radius 3 cm and height 4 cm. Find slant height and CSA.

• Slant height $l = \sqrt{3^2 + 4^2} = 5$

• CSA = $\pi rl = \frac{22}{7} \times 3 \times 5 = 47.14 \text{ cm}^2$

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✅ Key Points to Remember

• Use $\pi = \frac{22}{7}$ unless told otherwise

• TSA = CSA + area of base(s)

• Volume tells you capacity; Surface Area tells you exposure

• Practice unit conversions (cm³ to m³, etc.)

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📥 Download Chapter 13 PDF Notes: Coming Soon
📘 Previous Chapter: Chapter 12 – Areas Related to Circles »
📚 Next Chapter: Chapter 14 – Statistics »