# Math's: Meaning of Surface Area and Volume: Cuboids and Cubes

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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.

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 .

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

## 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 cm^{3}. 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 33.75m^{3}.

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 cm^{3} 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