Question

Tell me 3-Dimensional (3D) figures (shapes) formula like cone, cylinder etc...

Answer 1

Formulas of 3 Dimensional (3-D) Figures (Shapes) :-

Surface Area :

Types of surface area :-

1. Lateral surface area.
2. Curved surface area.
3. Total surface area.

★ Lateral surface area (L.S.A.) :-

1. Cube = 4a²

Where,

• a = side.

2. Cuboid = 2 (lb + bh) OR 2 (l + b) × h.

Where,

• l = length.
• b = breadth.
• h = height.

3. Area of four walls of a room = P × h = 2 (l + b) h.

Where,

• P = perimeter.
• l = length.
• b = breadth.
• h = height.

4. Area of (4 walls + ceiling) = lb + 2 (bh + hl) OR lb + 2 (b + l) h.

Where,

• l = length.
• b = breadth.
• h = height.

★ Curved surface area (C.S.A.) :-

1. Cylinder = P × height = 2πrh.

Where,

• P = perimeter
• r = radius.
• h = height.

2. Cone = πrl

Where,

• r = radius.
• l = length.

3. Sphere = 4πr²

Where,

• π = 22 / 7 OR 3.14
• r = radius.

4. Hemi-sphere = 2πr²

Where,

• π = 22 / 7 OR 3.14
• r = radius.

5. Hollow cylinder (pipe) = Inner curved surface area + Outer curved surface area = 2πh (r₁ + r₂)

Where,

• π = 22 / 7 OR 3.14
• h = height.
• r₁ = radius₁
• r₂ = radius₂

★ Total surface area (T.S.A.) :-

1. Cuboid = 2 (lb + bh + hl)

Where,

• l = length.
• b = breadth.
• h = height.

2. Cube = 6a²

Where,

• a = side.

3. Cylinder = 2πrh + 2πr² OR 2πr (r + h)

Where,

• π = 22 / 7 OR 3.14
• r = radius.
• h = height.

4. Cone = πrl + πr² OR πr (r + l)

Where,

• π = 22 / 7 OR 3.14
• r = radius.
• l = length.

5. Sphere = 4πr²

Where,

• π = 22 / 7 OR 3.14
• r = radius.

6. Hemi-sphere = 2πr² + πr² = 3πr²

Where,

• π = 22 / 7 OR 3.14
• r = radius.

7. Hollow cylinder = 2πh (r₁ + r₂) + 2π (r₁² – r₂²)

Where,

• π = 22 / 7 OR 3.14
• r₁ = radius₁
• r₂ = radius₂

★ Volumes :-

1. Cuboid = l × b × h

Where,

• l = length.
• b = breadth.
• h = height.

2. Cube = a³

Where,

• a = side.

3. Cylinder = πr²h

Where,

• π = 22 / 7 OR 3.14
• r = radius.
• h = height.

4. Cone = 1 / 3 πr²h

Where,

• π = 22 / 7 OR 3.14
• r = radius.

5. Sphere = 4 / 3 πr³

Where,

• π = 22 / 7 OR 3.14
• r = radius.

6. Hemi-sphere = 2 / 3 πr²

Where,

• π = 22 / 7 OR 3.14
• r = radius.