# Volume and Surface Area

**Cuboid**

If l, b and h are length, breadth and height of a cuboid, then

Volume = l×b×h

Surface are = 2 (lb +l>h +bh)

Lateral surface area = 2 (l +b)×h

Length of a diagonal = (l² +b² +c²)**Cube**

If a be the length of an edge of a cube, then

Volume = a³

Surface area = 6a²

Length of a diagonal = 3a

## Exercise

- If the surface area of a cube is 1176 cm², find

(i) the length of a diagonal

(ii) volume of the cube. - A closed rectangular wooden box has inner dimensions 90 cm by 80 cm by 70 cm. Compute its capacity and the area of the tin foil needed to line its inner surface.
- The lateral surface area of a cuboids is 224 cm². Its height is 7 cm and
the base is a square. Find

(i) a side of the square base

(ii) the volume of the cuboids. - The inner dimensions of a closed wooden box are 2 m by 1.2 m by 0.75 m. The thickness of the wood is 2.5 cm. Find the cost of wood required to make the box if 1 m³ of wood costs Rs 5400.
- A cube of 11 cm edge is immersed completely in a rectangular vessel containing water. If the dimensions of the base of the vessel are 15 cm× 12 cm, find the rise in the water level in centimeters correct to 2 decimal places, assuming that no water overflows.

## Answers

**1.**(i) 24.25 cm (ii) 2744 cm³

**2.**504000 cm³; 38200 cm²

**3.**(i) 8 cm (ii) 448 cm³

**4.**Rs 1350

**5.**7.39 cm