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.

Volume = 1/3 π*r*^{2}*h*. Surface Area (curved) = π *r* *l*, where *l* = slant height.

As per the Pythagoras theorem, *l*^{2} = *r*^{2} + *h*^{2}. formula for surface area (total) = π *r l* + π*r*^{2}.

1. 16(5/22)cm

2. 18(2/3)cm

3. 11(1/3)cm

4. 17(1/7)cm

5. 12(2/5)cm

Therefore we have, π x r x (r + l) = 217, which is same as π x 3.5 x (3.5 + l) = 217.

Therefore, the slant height = 16 5 / 22 cm.

1. 15(1/18)cu m

2. 16(2/21)cu m

3. 42(1/2)cu m

4. 58(2/3)cu m

5. 16(1/6)cu m

= (1/3) x π x 4 x 4 x 3.5

= 58 2/3 m

1. 327.38 cm^{3}

2. 256.67 cm^{3}

3. 392.5 cm^{3}

4. 102.6 cm^{3}

Must Read 3D Geometry Articles

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

A pyramid is a solid, whose lateral faces are triangular with a common vertex and whose base is a polygon. A pyramid is said to be tetrahedron (triangular base), square pyramid, hexagonal pyramid etc, according to the number of sides of the polygon that form the base.

In a pyramid with a base of n sides, number of vertices = n + 1.

Number of faces including the base = n + 1.

Surface area of lateral faces = 1/2 x perimeter of base x slant height

Total surface area of pyramid = Base area + 1/2 x perimeter of base x slant height

Volume of pyramid = 1/3 × Base area x height. A cone is also a pyramid.

In a pyramid with a base of n sides, number of vertices = n + 1.

Number of faces including the base = n + 1.

Surface area of lateral faces = 1/2 x perimeter of base x slant height

Total surface area of pyramid = Base area + 1/2 x perimeter of base x slant height

Volume of pyramid = 1/3 × Base area x height. A cone is also a pyramid.

Lateral surface of the pyramid = 1/2 x Base perimeter x slant height. Diagonal = 10 m ∴ side = 10/√2.

∴Base perimeter

(4x10)/√2 = 40√2. Also slant ht = √h

∴ Lateral Surface = (1/2) x (40/√2) x (15/√2) 150m