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1.

If a river of depthness 2 metres and breadth 45 metress, flowrs at a speed of 3 km per hours, then find the quanity of water that will fall from the river to the sea in 1 minute.

Answer» Speed of the river=3 km per hour `=(3 xx 1000)/(60)` metres // minute = 50 metres // minute. So, in 1 minutes the quanity of water that will fall from the river of the sea `=2 xx 45 xx 50 ` cubic metres = 4500 cubic metres.
Hence the required quatity of water `=4500 m^3 `
Discussion
2.

A canal of breadth 2m and depth 8 dcm have been drugged in our village Bakultala. If the volume of the soil extrated be 240 cubic-metres, then find the length of the canal.

Answer» Let the length of the canal be x metres. The breadth of the canal = 2 metres and the depth of the canal = 8 dcm = 0·8 metre. `therefore` the volume of the canal `= x xx 2 xx 0.8 ` cubic-metres `= 1.6 x = 240 rArr x = 240/1.6 = 150 `
Hence the length of the canal = 150 metres
Discussion
3.

The length , breath and height of a cuboidal hole are 40 m 12 m, and 16 m respectively, The number of planks having the height of 5 m , the breath of 4 m and the thickness of 2 m can be kept in that hole isA. 190B. 192C. 184D. 180

Answer» The volume of the hole `= 40 xx 12 xx 16 ` cubic -m
The volume of each of the planks `= (5 xx 4 xx 2 )` cubic -m
Hence the planks can be kept `=(40 xx 12 xx 16)/(5xx 4xx 2)`
`therefore` ( b) is correct .
Discussion
4.

The length of brass -plate of a square -shaped base is x cm, thickness 1 mm and weight 4725 gms. If the weight of 1 cu-cm brass is 8.4 gms then what will be the value of x ?

Answer» The area of the base of the brass-plate `=x^2` sq-cm.
Thickness = 1 mm =01 cm
`therefore` the volumes of the plate `=x^2xx 0.1 "cc "= x^2/10 "cc" `
, `therefore` the weight jof `(x^2)/(10)"cc" ` brass `= (8.4 xx x^2)/(100) 4725 ` or `84x^2` = 472500 or x `x^2 =5625 `
`x =sqrt(5625)= 75 `
Hence the value of x is 75
Discussion
5.

The length and breadth of a cuboid -shaped piece of wood are 2.3 metres and 0.75 metres respectively. If the volume of the wooden piece be 1.104 cubic-metres, then how may piece of wood of size `2.3m xx 0.75 m xx0.04m` can be cut off from this piece of wood ?

Answer» Let the thickness of the wooden piece by x metres.
Its volume = 1.104 cu-metres.
As per question, `2.3 xx 0.75 xx x=1.104`
`rArr x = 1.104/(2.3 xx 0.75)=(10xx 1104 xx100)/(23 xx 75 xx1000)= 0.64`
`:.` the thickness of the wooden piece = 0.64m.
Let the number of such piece of wood be y.
`:. 2.3 xx 0.75 xx 0.04 xx y=2.3 xx 0.75xx 0.64`
`rArr y= (2.3 xx0.75 xx 0.64)/(2.3xx0.75xx0.04)= 16`
Hence the required number of piece of wood = 16`.
Discussion
6.

8 wooden rectangular parallelopiped of same shape when arranged one over another, the volume becomes 128 cc. If the base of each rectangular parallelopipcd be a square and of height 1 cm, then find the length, breadth and height of each wooden rectangular parallelopiped.

Answer» Let the length and breadth of each wooden rectangular parallelopiped be x cm. Since · there are 8 such parallelopiped of height 1 cm each have been arranged one over another, the total height . of this soild object is 8 cm. ·
So, the volume of whole solid objecti `= x xx x xx 8 " cc" = 8x^2` cc
As per question `8x^2=128 or , x^2 = 128/8 = 16 or, x sqrt(16) ` or , x =4
Hence the length, breadth and height of each of the cuboidal solid are 4 cm, 4 cm and l cm respectively.
Discussion
7.

The length of a cuboidal tank is 20 metres. The height of the water- level in the tank decreases by 15 cm when 18 kilolitres water is taken out from the tank. Then find the breadth of the tank.

Answer» 18 kilolitres = 18 cubic- metres.
The height of water -level in the tank decreases by 15 cm = 0.15 metre.
Let the bredth of the tank be x metres,
`:. 20 xx x xx 0.15 = 18 or, x = 18/(20 xx 0.15)= 6`
Hence the breadth of the tank = 6 metres.
Discussion
8.

If the length of the diagonal of a cube be `4sqrt6`cm, then the length of the diagonal of each surface of the cube will beA. `8 sqrt2 cm`B. 8 cmC. `4sqrt2 cm`D. 4 cm

Answer» Correct Answer - A
Discussion