Question

an iron beam is 4m long ,40 cm broad and 30 cm thick. it's weight in kg . if 1 cu. cm of iron weights 8 cm is

Answer 1

i) Length = 12 m, Breadth = 10 m , height = 4.5 m

ii) Length = 4 m, Breadth = 2.5 m , height = 50 cm

iii) Length = 10 m, Breadth = 25 dm , height = 25 cm

Soln:

i) Length = 12 m

Breadth = 10 m

Height = 4. 5 m

Volume of the cuboid = length x breadth x height = 12 x 10 x 4.5 = 540 m3

ii) Length = 4 m

Breadth = 2.5 m

Height = 50 cm

= 50100 m ( therefore, 1 m = 100 cm )

Volume of the cuboid = length x breadth x height = 4 x 2.5 x 0.5 = 5 m3

Q 2. Find the volume in cubic decimeter of each of the cubes whose side is :

i) 1.5 m

ii) 75 cm

iii) 2 dm 5 cm

Soln :

i) Side of the cube = 1.5 m

= 1.5 x 10 dm ( Because 1 m = 10 dm )

= 15 dm

Therefore, Volume of the cube = (side)3 =  (  15 )3 = 3375 dm3

ii) Side of the cube = 75 cm

= 75 x 110  dm ( because 1 dm = 10 cm )

= 7.5 dm

Therefore, Volume of the cube = ( side )3 = ( 7.5 )3 = 421.875 dm3

iii) Side of the cube = 2 dm 5 cm

= 2 dm + 5 x 110 dm ( Because 1 dm = 10 cm )

= 2 dm + 0.5 dm = 2.5 dm

Therefore, Volume of the cube = ( side )3 = ( 2.5 )3 = 15.625 dm3

Q3. How much clay is dug out in digging a well measuring 3 m by 2 m by 5 m ?

Soln:

The measure of well is 3 m x 2 m x 5 m

Therefore, volume of the clay dug out = ( 3 x 2 x 5 ) m3 = 30 m3

Q4. What will be the height of cuboid of volume 168 m3 , if the area of its base is 28 m2 ?

Soln:

Volume of the cuboid = 168 m3

Area of its base = 28 m2

Let h m be the height of the cuboid.

Now, we have the following :

Area of the rectangular base = length x breadth

Volume of the cuboid = length x breadth x height

Volume of the cuboid = ( area of the base ) x height

168 = 28 x h

h = 16828 = 6 cm

Therefore, the height of the cuboid is 6 m.

Q 5. A tank is 8 m long, 6 m broad and 2 m high. How much water can it contain ?

Soln:

Length of the tank = 8 m

Breadth = 6 m

Height = 2 m

Therefore, Its volume = length x breadth x height = ( 8 x 6 x 2 ) m3 = 96 m3

We know that 1m3 = 1000 L

Now, 96 m3 = 96 x 1000 L = 96000 L

Therefore, the tank can store 96000 L of water.