Volume of a Cuboid

Q. Question 8
Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes, if 8 cm of standing water is needed?

Q. Question 10
500 persons are taking a dip into a cuboidal pond which is 80 m long and 50 m broad. What is the rise of water level in the pond, if the average displacement of the water by a person is $0.04m^3$ ?

Q. The volume of a cuboid of length l, breadth b and height h is _______.

1. lb+ bh+hl
2. lbh(l+b+h)
3. lbh
4. lb

Q.

A canal is 300 cm wide and 120 cm deep.The water in the canal is flowing with a speed of 20 km/hr. How much area will it irrigate in 20 minutes if 8 cm of standing water is desired?

Q.

Three metallic solid cubes whose edges are 3 cm, 4 cm and 5 cm are melted and formed into a single cube. Find the edge of the cube so formed.

Q.

The area of the base of a rectangular tank is 6500 $c{m}^2$ and the volume of water contained in it is 2.6 $m^3$. The depth of water in the tank is

(a) 3.5 m (b) 4 m (c) 5 m (d) 8 m

Q.

A river 1.5 m deep and 36 m wide is flowing at the rate of 3.5 km/hr. Find the amount of water (in cubic metres) that runs into the sea per minute.

Q.

Question 11
A mason constructs a wall of dimensions 270 cm×300 cm×350 cm with the bricks each of size $22.5cm\times 11.25cm\times 8.75cm$ and it is assumed that $\frac{1}{8}$ space is covered by the mortar. Then, the number of bricks used to construct the wall is

Thinking process- If we divide the volume of the wall except for the volume of mortar used on the wall by the volume of one brick, then we get the required number of bricks used to construct the wall.
(A) 11100
(B) 11200
(C) 11000
(D) 11300

Q.

Question 13
A wall 24 m long, 0.4 m thick and 6 m high is constructed with the bricks each of dimensions $25cm\times 16cm\times 10cm$. If the mortar occupies $\frac{1}{10}th$ of the volume of the wall, then find the number of bricks used in constructing the wall.

Q.

The length, breadth and height of a cuboid are 2 m, 5 m and 4m respectively.
1) What is the difference between total surface area and curved surface area ?
2) If a cube of side measuring 100cm is placed inside the cuboid, what is amount of void space in the cuboid? [4 MARKS]

Q.

500 persons have to dip in a rectangular tank which is 80 m long and 50 m broad. What is the rise in the level of water in the tank, if the average displacement of water by a person is 0.04 $m^3$ ?

Q.

Which of the following equations represent the correct relation among mass, density and volume?

1. Density = Mass × Volume
2. Mass = Density × Volume
3. Volume = Density × Mass
4. A for solids and B for liquids & gases

Q.

Five identical cubes, each of edge 5 cm, are placed adjacent to each other. Find the volume of the resulting cuboid.

Q.

Find the ratio of surface area of a cuboid to the volume if the length is 2 times of breadth which is 2 times of height which is 2 cm.

1. 7: 2

2. 7: 4

3. 3 : 2

4. 3 : 4

Q.

A cuboidal water tank measuring 80 cm × 60 cm × 60 cm is filled from a pipe of cross sectional area 1.5 $c{m}^2$. If speed of water is 3.2 m/s, then how long does it take to fill the tank?

1. 5 mins

2. 10 mins

3. 12 mins

4. 15 mins

Q.

In a shower, 5 cm of rain falls. The volume of the water that falls on 2 hectares of ground, is

(a) 100 $m^3$ (b) 10 $m^3$ (c) 1000 $m^3$ (d) 10000 $m^3$

Q.

The bottom, side and front areas of a rectangular box are known. The product of these area s is equal to

1. The volume of the box

2. The square root of the volume

3. Twice the volume

4. The square of the volume

Q.

A pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins, respectively.The dimension of the cuboid are $10cm\times 5cm\times 4cm$.The radius of each of the conical depression is 0.5 cm and the depth is 2.1 cm.The edge of the cubical depression is 3cm.Find the volume of the wood in the entire stand.

Q. Question 4
A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.

Q.

Find the height of the cuboid whose length, breadth and volume are $35cm$, $15cm$ and $14175c{m}^3$, respectively.

Q.

Question 2

Only one of the four options is correct. Write the correct one.

The ratio of the number of sides of a square to the number of edges of a cube is

a) 1 : 2

b) 3 : 2

c) 4 : 1

d) 1 : 3

Q.

A box has length, breadth and height of $10cm,$ $20cm$ and $5cm$ respectively. The lateral surface area of the box is equal to

1. 100 cm²

2. 200 cm²

3. 300 cm²

4. 400 cm²

Q.

A small indoor greenhouse is made entirely of glass panes held together with tape. It is 30 cm long, 25 cm wide and 25 cm high. Find the length of the tape needed to cover all the 12 edges.

1. 320 cm

2. 302 cm

3. 203 cm

4. 230 cm

Q. Match the following cubes of given side with the number of cubes formed by cutting a cube of volume 512 m³

1. 512
2. 64
3. 8
4. 1

Q. There is a thin metal plate of length and breadth 2M mm and 2K mm respectively. Its thickness is 1 mm. If ‘N’ number of plates are placed one on top of the other, what is the object formed and what is its volume in $m{m}^3$?

1. Cuboid, MKN
2. Cuboid, 4MKN
3. Sphere, 4MKN
4. Cylinder, 2 MKN

Q. If a cuboidal carton has length 80 cm, breadth 40 cm and height 60 cm, then the volume of the carton is .

1. $192000c{m}^3$
2. $100000c{m}^3$
3. $2000c{m}^3$
4. $19200c{m}^3$

Q. There is a thin metal plate of length and breadth 2M mm and 2K mm respectively. Its thickness is 1 mm. If ‘N’ number of plates are placed one on top of the other, what is the object formed and what is its volume in $m{m}^3$?

1. Cuboid, MKN
2. Cuboid, 4MKN
3. Sphere, 4MKN
4. Cylinder, 2 MKN

Q. A cuboid is 30 cm long , 25 cm broad, and 5 cm high . How much of its volume will differ from that of a cube of edge 16 cm?

1. 346 cm${}^3$ more than the volume of cube.
2. 246 cm${}^3$ less than the volume of cube.
3. 346 cm${}^3$ less than the volume of cube.
4. 246 cm${}^3$ more than the volume of cube.

Q.

Which among the following is the largest ?

1. l

2. 

3. 

4. 

Q.

Find the cost of digging a cuboidal pit $8m$ long, $6m$ broad, and $3m$deep at the rate of $Rs30$per $m^3$