Volume of Cuboid

Q. Find the surface area of a sphere, if its volume is 38808 cubic cm.($\mathrm{\pi }=\frac{22}{7}$)

Q. Find the radius of a sphere if its volume is 904.32 cubic cm. ($\mathrm{\pi }$= 3.14)

Q.

$\mathrm{The}\mathrm{volume}\mathrm{of}a\mathrm{wall},5\mathrm{times}\mathrm{as}\mathrm{high}\mathrm{as}\mathrm{it}\mathrm{is}\mathrm{wide}\mathrm{and}8\mathrm{times}\mathrm{as}\mathrm{long}\mathrm{as}\mathrm{it}\mathrm{is}\mathrm{high},\mathrm{is}12.8\mathrm{cu}.\mathrm{meters}.\mathrm{Find}\mathrm{the}\mathrm{breadth}\mathrm{of}\mathrm{the}\mathrm{wall}\mathrm{in}\mathrm{cm}.$

1. 40

Q.

$\mathrm{The}\mathrm{volume}\mathrm{of}a\mathrm{wall},5\mathrm{times}\mathrm{as}\mathrm{high}\mathrm{as}\mathrm{it}\mathrm{is}\mathrm{wide}\mathrm{and}8\mathrm{times}\mathrm{as}\mathrm{long}\mathrm{as}\mathrm{it}\mathrm{is}\mathrm{high},\mathrm{is}12.8\mathrm{cu}.\mathrm{meters}.\mathrm{Find}\mathrm{the}\mathrm{breadth}\mathrm{of}\mathrm{the}\mathrm{wall}\mathrm{in}\mathrm{cm}.$

1. 40

Q.

Find the volume of a box of length $80cm$, breath $50cm$ and depth 40 cm in $m^3$.

Q. Find the height(in metres) of the cubical tank that contains 27, 000 liters of water in it.

1. 3

Q.

Volume of the largest cut diamond is 1.84 cubic inches. What is its volume in cubic centimetre and cubic metres? [1 inch = 2.54 cm]

Q. Find:

Q.

The diameter of a right circular cylinder is decreased by $10\%$ The volume of the cylinder remains the same then the percentage increase in height is:

1. $20\%$

2. $23.45\%$

3. $5\%$

4. $20.5\%$

Q.

A hexagonal hole with each side 2m is dug in a school ground to collect rain water. It is 5m deep. Currently it has water, 1 m deep. How much water is collected in the hole?

1. $6\sqrt{3}{m}^3$

2. $6m^3$

3. $5\sqrt{3}{m}^3$

4. $4\sqrt{3}{m}^3$

Q.

The volume of a cone of radius $12cm$ and slant height $20cm$ is $16896c{m}^3$.

1. True

2. False

Q.

Question 2
A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold? $(1m^3=1000l)$

Q.

A piece of metal in the form of a cone of radius $\mathbf{3}\mathbf{}\mathbf{cm}$ and height $\mathbf{7}\mathbf{}\mathbf{cm}$ is melted and cast into a cube. Find the side of the cube.

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

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

Q. The time taken to empty a water tank of capacity $1024m^3$ at the rate of $64\frac{m^3}{min}$ is .

1. 16 minutes
2. 24 minutes
3. 32 minutes

Q.

Question 3
A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?

Q. Find the volume of a cuboid whose length is 24 cm , breadth is 12 cm and height is 13 cm.

1. $37454c{m}^3$
2. $3764c{m}^3$
3. $3744c{m}^3$
4. $3794c{m}^3$

Q.

Water is flowing at the rate of 15 km/hr through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Find the time in which the level of water in the tank will rise by 21 cm.

1. 4 hrs

2. 5 hrs

3. 3 hrs

4. 2 hrs

Q.

The picture below is of a water trough:-

The front and back faces are identical isosceles trapeziums. How many litres of water can it hold?

1. 766 $m^3$.

2. 1242 litres.

3. 875 litres.

4. 1000 litres.

Q.

The radius and height of a right circular cone are in the ratio $1:2$. If its volume is $144\pi {cm}^3$, find its slant height.

1. 5 $\sqrt{5}$ cm

2. 6 $\sqrt{5}$ cm

3. 4 $\sqrt{5}$ cm

4. 5 $\sqrt{6}$ cm

Q.

Find the volume of a cubical box whose surface area is 13.50 cm².

1. 9.1000 cm³

2. 8.475 cm³

3. 3.375 cm³

4. 3.750 cm³

Q. The volume of a wall, 5 times as high as it is wide and 8 times as long as it is high, is 12.8 cu. meters. Find the breadth of the wall.

1. 40 cm
2. 30 cm
3. 20 cm
4. 10 cm

Q. Arrange the following cylindrical and cuboidal shaped containers in increasing order of their volume.

1. R=r, H=h
2. R=2r, H=$\frac{h}{2}$
3. R=2r, H=h
4. L=r, B=r, H=h

Q. If V is the volume of a cuboid of dimensions x, y, z and A is its surface area, then $\frac{A}{V}$

(a) x²y²z²

(b) $\frac{1}{2}\left(\frac{1}{xy}+\frac{1}{yz}+\frac{1}{zx}\right)$

(c) $\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)$

(d) $\frac{1}{xyz}$

Q. Milk is pouring into a reservoir at the rate of 90 litres per minute. If the volume of reservoir is 108 m${}^3$. Find the number of minutes it will take to fill the reservoir.

1. 1600 minutes
2. 1200 minutes
3. 1400 minutes
4. 2000 minutes

Q. Find the volume of cuboid with 6 cm, 8 cm, 10 cm as its dimensions

Q. Find the area of the base of a cuboid if its volume is 48 cubic m and its height is 4 m.

1. 16 sq. m
2. 12 sq. m
3. 44 sq. m
4. 24 sq. m

Q. A match box measures $4\text{cm}\times 2.5\text{cm}\times 1.5\text{cm}.$ Volume of a packet containing 12 such boxes (no space is left in the packet) is ____________.

1. $170{\text{cm}}^3$
2. $150{\text{cm}}^3$
3. $180{\text{cm}}^3$
4. $120{\text{cm}}^3$

Q. A cuboidal tank can hold 650 litres of milk. If it is 130 cm long and 250 cm wide, then the height of the tank is .

1. 20 cm
2. 25 cm
3. 30 cm

Q. If V is the volume of a cuboid of dimensions a, b, c and S is its surface area, then prove that

$\frac{1}{V}=\frac{2}{S}\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)$