Math՚s: Meaning of Surface Area and Volume: Cuboids and Cubes (For CBSE, ICSE, IAS, NET, NRA 2022)

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Meaning of Surface Area and Volume

The terms surface area and volume are used in connection with solid figures.

  • The surface constituting the solid is called the surface area of the solid figure. Surface area is measured in square units such as etc.
  • The space region enclosed by the solid figure is called the volume of the solid figure. Volume is measured in cubic units such as etc.

Cuboids and Cubes

Cuboids- Cuboid is a solid figure with six rectangular flat faces (ABCD, EFGH, DCGH, ABFE, BCGF & ADHE) ; twelve edges (AB, BC, CD, AD, EF, FG, GH, EH, AE, BF, CG & DH) and eight vertices (A, B, C, D, E, F, G & H) . Ex- Match Box, Brick etc.

Cuboids and Cubs

At each vertex, three edges meet. One of these three edges is taken as the length , the second as the breadth and third is taken as the height (or thickness or depth) of the cuboid.

  • Surface Area: Total Surface Area-
  • Lateral Surface Area:
  • Volume:
  • Diagonal:

Cubes- Cube is a special type of cuboid where all the six faces are of square shapes of equal sides .

Cuboids and Cubs
  • Surface Area: Total Surface Area-
  • Lateral Surface Area:
  • Volume:
  • Diagonal:

Right Circular Cylinder

Right Circular Cylinder

A solid figure having a curved lateral surface closed with two flat circular ends (top & bottom faces) is known as a right circular cylinder.

Surface Area- Curved/Lateral:

Total Surface Area:

Volume:

Volume of Hollow Cylinder:

1. Find the edge of a cube whose volume is 3375 cm3. Also, find its surface area.

Solution- Let the edge of the cube be ,

Then,

2. Find the length and surface area of a wooden plank of width 3m, thickness 75 cm and volume 33.75m3.

Solution- The units of all the dimensions have to be same, so thickness of the wooden plank will be converted into meter.

Let the length of the wooden plank be .

3. Volume of a right circular cylinder is 3080 cm3 and radius of its base is 7 cm. Find the curved surface area of the cylinder.

Solution- Let the height of the cylinder be cm

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