L-02, Ch-11th, SA&V, Practice Questions P1, Surface Area of Cones.

Описание: 📘 Class 9 Maths Chapter 11 – Surface Areas and Volumes | Full Chapter Summary

In this chapter, “Surface Areas and Volumes”, we study formulas to find the surface area and volume of 3D solid shapes like cuboids, cubes, cylinders, cones, spheres, and hemispheres. This chapter helps us understand the relationship between 2D and 3D geometry and is widely used in real-life problems involving containers, tanks, pipes, and packaging.


🔹 1. Basic 3D Shapes and Their Terms

Cuboid → Box-shaped solid with 6 rectangular faces.

Cube → Special cuboid with all edges equal.

Cylinder → Two parallel circular bases connected by a curved surface.

Cone → Circular base with a single vertex (like an ice-cream cone).

Sphere → Perfectly round solid (like a ball).

Hemisphere → Half of a sphere.


🔹 2. Surface Areas of Solids


Cuboid (l, b, h)

LSA. = 2h(l + b)

TSA. = 2(lb + bh + hl)


Cube (a)

LSA. = 4a²

TSA. = 6a²


Right Circular Cylinder (r, h)

CSA. = 2πrh

TSA. = 2πr(h + r)


Right Circular Cone (r, l)

CSA. = πrl

TSA. = πr(l + r)


Sphere (r)

SA= CSA =TSA =  4πr²


Hemisphere (r)

CSA. = 2πr²

TSA. = 3πr²


🟢 Note:

LSA (Curved Surface Area) → Area of curved or side part only.

TSA (Total Surface Area) → Includes both curved area and bases.


🔹 3. Volumes of Solids


Cuboid. = l × b × h


Cube.     = a³


Right Circular Cylinder.  = πr²h


Right Circular Cone.  = (1/3)πr²h


Sphere.  = (4/3)πr³


Hemisphere.   = (2/3)πr³


🔹 4. Conversion of Solids (Combination and Transformation)

When solids are melted or reshaped, Volume before = Volume after.

Used to solve questions where one solid is converted into another (e.g., melting a sphere into smaller spheres or reshaping a cone into a cylinder).


🔹 5. Real-life Applications

Finding surface area → Painting, wrapping, or covering objects.

Finding volume → Filling water, air, or material in containers.

Used in construction, packaging, manufacturing, and design.


🎯 Key Learning Outcomes

Understanding and applying formulas for surface areas and volumes.

Converting units between cm³, m³, and liters.

Solving practical problems on melting and recasting solids.

Strengthening geometric visualization of 3D shapes.

Building strong conceptual base for Class 10 “Mensuration.”


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