Most tests often include questions based on the knowledge of the geometries of 3-D objects such as cylinder, cone, cuboid, cube & sphere. The purpose of the article is to help you learn basics of 3-D geometry and encapsulate some of the important formulae and tricks.

The questions on Volume and Surface Area appear in all the competitive exams. Most of the students tend to avoid this topic considering it to be quite complex and calculative. This article would help you not only in memorizing the formulas, but also in understanding direct or indirect applications of these formulas. We strongly advice you go through each and every definition and formula given below to solve questions on Surface Area and Volume.

For any regular solid, Number of faces + Number of vertices = Number of edges + 2. This formula is called Euler’s formula.

The surface area of a rectangular solid is equal to the sum of the areas of all the faces.

Total surface area = 2(lb + bh + hl )

Curved surface area = 2h(l + b)

Total surface area = 2(lb + bh + hl )

Curved surface area = 2h(l + b)

Volume = lbh, Where l= length, b= breadth, h= height

In the rectangular solid, the dimensions are 3, 4, and 8.

The surface area of the rectangular solid is equal to 2[(3 × 4) + (3 × 8) + (4 × 8)] = 136.

The cuboid volume is equal to 3 × 4 × 8 = 96.

Body diagonal of a cuboid = Length of the longest rod that can be kept inside a rectangular room is =√L

1. 1200 cm^{2}

2. 1000 cm^{2}

3. 1100 cm^{2}

4. 600 cm^{2}

Explanation: Here length of cuboid = 20 cm.

Breadth and height of cuboid = 10 cm.

∴TSA = 2(L*B + B*H + H*L)

surface area = 2(200 + 100 + 200) = 1000 cm^{2}

Breadth and height of cuboid = 10 cm.

∴TSA = 2(L*B + B*H + H*L)

surface area = 2(200 + 100 + 200) = 1000 cm

Must Read 3D Geometry Articles

- Mensuration-Cone & Pyramid
- Mensuration-Solved Examples
- Mensuration- Sphere & Hemisphere
- Mensuration- Right Prism & Cylinder

- Mensuration-Cube & Cuboid
- Mensuration Practice Problems: Level 01
- Mensuration Practice Problems: Level 02

cube Volume = a

Surface Area formula = 6a^{2}, where a is the side of a cube.

Body Diagonal = Length of the longest rod inside a cubical room = a√3

Body Diagonal = Length of the longest rod inside a cubical room = a√3

1. 18 cm

2. 24 cm

3. 12 cm

4. 36 cm

Explanation: Volume = 1.7 litres = 1.7 x 1000 = 1700 cm^{3}.

∴Edge = (1700)^{1/3} = 12 cm.

∴Edge = (1700)

1. 27,000

2. 400

3. 8,000

4. 800

Explanation: Surface area of larger cube = 486cm^{2}

∴6L^{2} = 486 ⇒ L^{2} = 81 ⇒ L = 9cm.

∴ Volume of larger cube = 9 x 9 x 9 = 729 cm^{3}. Surface area of smaller cube = 54mm^{2} = 54/100 cm^{2}. ∴6l^{2} = 54/100 ⇒ l^{2} = 0.09 ⇒ 1 = 0.3cm.

Volume of smaller cube = 0.3 x 0.3 x 0.3

= 0.027 cm^{3}.

&there; x = 729/0.027 = 27000.

∴6L

∴ Volume of larger cube = 9 x 9 x 9 = 729 cm

Volume of smaller cube = 0.3 x 0.3 x 0.3

= 0.027 cm

&there; x = 729/0.027 = 27000.