Volume of Cuboids

Q.

A swimming pool is $200m\times 50m$ and has an average depth of $2m$. By the end of a summer day, the water level drops by $2cm$. How many cubic metres of water is lost on the day?

Q.

A square plat of side $xcm$ is $8mm$ thick .if its volume is $2880c{m}^3,$, find the value of $X.$

Q. If V is the volume of a cuboid of dimensions a × b × c and A is its surface area, then $\frac{A}{V}$ is

1. $a^2{b}^2{c}^2$
2. $\frac{1}{abc}$
3. $\frac{1}{2}(\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca})$
4. $2(\frac{1}{a}+\frac{1}{b}+\frac{1}{c})$

Q. A water tank is 1.5 m long, 1 m wide and 0.6 m deep. Find the volume of the tank in litres.

1. $1080\text{litres}$
2. $900\text{litres}$
3. $960\text{litres}$
4. $950\text{litres}$

Q.

Two cubes of edge 14 cm each are joined end to end to form a cuboid. Find the volume of the cuboid.

1. $5469c{m}^3$
2. $5588c{m}^3$
3. $5488c{m}^3$
4. $6488c{m}^3$

Q. A cuboidal milk tank is 1.2 m long, 1m wide and 0.6 m deep. Find the capacity of the tank in litres.

1. 420 litres
2. 620 litres
3. 720 litres
4. 520 litres

Q. A tank is in the shape of a cuboid of length 60 cm and width 50 cm. What should be its height to hold 4.5 litres of water? [Volume = capacity]

1. 1.3 $cm$
2. 1.6 $cm$
3. 1.8 $cm$
4. 1.5 $cm$

Q. In a cuboid if the length is doubled, height is tripled and breadth remains constant, then how many times does the volume becomes of its initial volume?

1. 6
2. 4
3. 5
4. 8

Q.

If we increase the length of a cuboid to 2 times the initial, What is the volume of the new cuboid?

1. 2 times the initial

2. 3 times the initial

3. one-half of the initial

4. Same as of that of the initial

Q.

The length and breadth of a room are in the ratio $4:3$ and its height is $5.5metres$. The cost of decorating its walls (including doors and windows) at $₹6.60$ per square metre is $₹5082$. Find the length and breadth of the room.

Q. Find the height of the cuboid, if its volume and base area are 275 cm${}^3$ and 25 cm${}^2$ respectively.

1. 11 cm
2. 12 cm
3. 14 cm
4. 13 cm

Q. A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold?

1. 135000
2. 136000
3. 125000
4. 145000

Q.

1 m ² is the area of a………….with a side 1 metre.

Q. A water tank is 1.4$m$ long. Im wide and 0.7$m$ deep. then the volume of the tank in litres

1. 860 litres
2. 780 litres
3. 980 litres
4. none of these

Q.

A lorry carrier measures $10\text{m}\times 7\text{m}\times 5\text{m}.$ Find the maximum number of wooden crates each measuring $2\text{m}\times 1\text{m}\times 0.5\text{m}$ that can be transported inside the lorry.

1. 668

2. 350

3. 588

4. 1024

Q. Find the volume of a cuboidal block of length 26 cm, breadth 13 cm and height 9 cm.

1. 3042 cm${}^3$
2. 3242 cm${}^3$
3. 3052 cm${}^3$
4. 4042 cm${}^3$

Q. If the volume of a marble box of dimensions 28 x 5 x h is 280 units, then what is the value of h?

1. 2
2. 7.5
3. 6
4. 6.5

Q. Milk is pouring into a cuboidal reservoir at the rate of 60 litres per minute. If the volume of reservoir is $108m^3$. Find the number of hours it will take to fill the reservoir.

1. 40
2. 30
3. 35
4. 38

Q.

Two cubes of edge 14 cm each are joined end to end to form a cuboid. Find the volume of the cuboid.

1. $5488c{m}^3$
2. $5588c{m}^3$
3. $5469c{m}^3$
4. $6488c{m}^3$

Q. Match the unknown $x$, for a cuboid of length l, breadth b, height h and volume v (all measures in cm).

1. 336 cm${}^3$
2. 2 cm
3. 8 cm
4. 3 cm

Q.

A metal sheet of thickness $2\text{cm}$ was used to make a container of external dimensions $30\text{cm}\times 15\text{cm}\times 25\text{cm}$ which is open from above. Find the volume of the container.

1. $6578{\text{cm}}^3$

2. $11250{\text{cm}}^3$

3. $12250{\text{cm}}^3$

4. $4672{\text{cm}}^3$

Q. If the volume of a cuboid is 729 m${}^3$and the area of the base is 162 m${}^2$, then find the height of the cuboid.

1. 4.5 m
2. 6.5 m
3. 5.5 m
4. 7.5 m

Q. A village has a population of 4000, requires 150 litres water per head per day. It has a tank measuring 20 m, 15 m, 6 m. How many days for the water is sufficient enough once the tank is made full.
[3 marks]

Q. A cuboidal petrol tank is $30$ cm long, $30$ cm wide and $1m$ $60cm$ high. It has petrol upto a height of $40cm$. How much more cubic cm of petrol can the tank contain?

Q. A rectangular tank containing water is $5$ m long, $3$ m broad and $2$ m deep. Find how much the water will rise, if a block of lead $1$m x $45$ cm x $30$ cm is put in the tank?

1. $9$ cm
2. $90$ cm
3. $9$ mm
4. $9$ m

Q. The number of blocks of dimensions $(4\text{m}\times 50\text{cm}\times 20\text{cm})$ that can be stored in a pit which is 19 m long, 13 m wide and 4 m deep is _____________.

1. 2430
2. 2470
3. 2420
4. 2450

Q. Circumference of the circle is given by .

1. $2\pi r$
2. $\pi r^2$
3. $2\pi r^2$
4. $2\pi d$

Q. How many bricks of 48 cubic units can be stored in a room of dimensions 12 x 4 x 10?

1. 15
2. 12
3. 10
4. 18

Q.

Find the volume of a cuboid of length 20 cm, breadth 15 cm and height 10 cm. ___

Q. A cubic metre of copper weighing $9000$ kilograms is rolled into a square bar $9$ metres long. An exact cube is cut off from the bar. How much does it weigh?

1. $=333\frac{1}{3}kg$
2. $=336\frac{1}{6}kg$
3. $=335\frac{1}{5}kg$
4. $=332\frac{1}{3}kg$