# Solved Examples

Surface area = 2(lb + bh + hl)

By putting all the values, we get surface area = 1.5 cu. m

If the surface area of a cube is 96 sq cm, find its volume.

The surface area of cube = 6 a^{2}, where a is the side of cube

So, 96 = 6 a^{2}

= > a^{2} = 16 = > a = 4 cm; Volume of the cube = a^{3} = 64 cu cm.

Length of tank = 50 m

Breadth of tank = 40 m

Let depth of the tank be x m = > 50 Ã— 40 Ã— x = 60,000 = > x = 30 m; Hence depth of the tank = 30 m.

If the volume of cube is 2197 cu cm, find the surface area and the length of the main diagonal of the cube.

Volume of cube = (side)^{3}

= > 2197 cu cm = (13)^{3} cu cm = > Side of cube = 13 cm

Surface area of cube = 6 (side)^{2} sq units = 6(13)^{2} sq cm = 1014 sq cm

Length of the diagonal of a cube = âˆš3 (side) = 3.13 cm = 13 3 cm or 22.516 cm.

b = 16 cm

h = 16 cm

= > Surface area of the resulting cuboid = 2(lb + bh + hl)

= 2(80 Ã— 16 + 16 Ã— 16 + 16 Ã— 80) sq cm = > 2(1280 + 256 + 1280) sq cm = 5632 sq cm.

A wooden box 1.5 m long, 1.25 m wide and 65 cm deep and open at the top is to be made. Determine the cost of wood required for it, if one sq m of wood costs Rs. 10.

Surface area of wood required

= lb + 2bh + 2lh [Q The box has five faces]

= 1.5 Ã— 1.25 + 2(1.25 Ã— .65 + 1.5 Ã— .65) sq cm

= 1.875 + 2 Ã— 0.65 Ã— 2.75 sq cm

= 1.875 + 3.575 = 5.450 sq cm.

= > Cost of wood required for the box = Rs. (5.45 Ã— 10) = Rs. 54.50.

Since the wood is 1 cm thick, so the internal dimension will be (42 â€“ 2) cm, (32 â€“ 2) cm, (27 â€“ 2) cm

= > Volume = (40 Ã— 30 Ã— 25) cu cm = 30000 cu cm.

A field is 600 m long and 50 m broad. A tank 30 m long, 20 m broad and 12 m deep is dug in the field. The earth taken out of it is spread evenly over the field. Find the height of the field raised by it.

Area of the field = (600 Ã— 50) sq m = 30000 sq m

Area of the tank = (30 Ã— 20) sq m = 600 sq m

Volume of earth taken out of tank

= (30 Ã— 20 Ã— 12) cu m

= 7200 cu m

Area of the field, where the earth is to be spread

= (30,000 â€“ 600) sq m = 29400 sq m

- Height of the field raised = 7200/29400 m = 12/49 m