Volume and Capacity

Q.

A cylindrical road roller made of iron is $1m$ wide. Its inner diameter is $54cm$ and the thickness of the iron sheet rolled into the road roller is $9cm$. Find the weight of the roller, if $1c.c$ of iron weighs$8gm$.

Q. A cubic cm of gold is drawn into a wire 0.1 mm in diameter, find the length of the wire.

Q.

The volume of a liquid that can be stored in a container is called its capacity.

1. True
2. False

Q. Arrange the solids in ascending order (from top to bottom) of volumes, where $l=b=h=r$.

1. Cuboid
2. Cone
3. Cylinder
4. Sphere

Q. Question 6
Write ‘True’ or ‘False’ and justify your answer in the following
The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the figure is $\frac{\pi r^2}{3}[3h-2r]$

Q.

A cylindrical saline bottle has a radius of 7 cm and height of 20 cm. If the saline is released at a rate of 10 cubic cm per second, in approximately how many minutes does the saline bottle get emptied? [2 MARKS]

Q.

Explain the term capacity?

Q.

Outer surface area of a hollow iron sphere is $1256c{m}^2$. If the thickness of iron is $1cm$, find the volume of air inside the sphere. Take $\pi =3.14$

1. $3052.08c{m}^3$​

2. $3051.08c{m}^3$​

3. $3053.08c{m}^3$​

4. $3054.08c{m}^3$​

Q.

Outer surface area of a hollow iron sphere is $1256c{m}^2$. If thickness of iron is $1cm$, find the volume of air filled inside the ball (assume $\pi =3.14$).

1. $3052.08c{m}^3$​
2. $3051.08c{m}^3$​
3. $3053.08c{m}^3$​
4. $3054.08c{m}^3$​

Q. Question 8
Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm?

Q. What is the volume of a cube having length of 2 m, breadth of 5 m and height of 3 m?

1. 10 cu. m
2. 15 cu. m
3. 6 cu. m
4. 30 cu. m

Q. The capacity of a closed cylindrical vessel of height 1 m is 15.4 l. How many square metres of the metal sheet would be needed to make it? [3 MARKS]

Q. Density and mass of the solid block is $5.2kg/m^3$ and $2kg$.Find its volume?

1. $0.3846m^3$
2. $7846c{m}^3$
3. $68.46c{m}^3$
4. $98.46c{m}^3$

Q. The volume of material required to be extracted from a sphere of radius 4 cm to create a shell of radius 1 cm = cm ${}^3$.

1. 264
2. 288
3. 464
4. 512

Q.

Differentiate between volume and capacity.

Q.

Explain the relation between the different units of volume and capacity.

Q.

Outer surface area of a hollow iron sphere is $1256c{m}^2$. If the thickness of iron is $1cm$, find the volume of air filled inside the ball.

1. 3052.08 cm³
2. 3051.08 cm³
3. 3053.08 cm³
4. 3054.08 cm³

Q. The dimensions of a rectangular block with Vermeer calliper having least count 0.1mm 5.0mm10.0mm10.0mm the maximum percentage error in the measurement of volume of the block is

Q.

Find the volume of : [2 MARKS]

Q.

Outer surface area of a hollow iron sphere is $1256c{m}^2$. If the thickness of iron is 1 cm, find the volume of air filled inside of the ball.

1. 3052.08 cm³
2. 3051.08 cm³
3. 3054.08 cm³
4. 3053.08 cm³

Q. The capacity of a right circular cylinderical tank of radius 7 cm and height 14 cm = $\times {10}^{-4}{m}^3$.

1. 21.56
2. 2.156
3. 215.6
4. 0.2156

Q. The school nurse at Pine Street High School surveyed the heights of all of the female students at the school. The median of the heights was $165$ centimeters and the mode was $162$ centimeters. Which of the following statements must be true?

1. The height of half of the female students is $165$ centimeters.
2. The most frequently occurring height of the female students is $162$ centimeters.
3. The average (arithmetic mean) of the heights of the female students is $163.5$ centimeters.
4. More female students are shorter than $165$ centimeters than are taller than $165$ centimeters.
5. More female students are $165$ centimeters tall than $162$ centimeters tall.

Q.

Use the following information to answer the next question.

What is the volume of the given figure? (Use π = ²²/₇)

1. (¹⁸³⁵⁶/₇) L

2. (²⁴⁵¹²/₇) L

3. (²²⁰²²/₃) L

4. (²³¹⁶²/₃) L

Q.

One cubic centimeter of a typical cumulus cloud contains 50-500 water drops, which have a typical radius of 10 micro meter. For that range, give the lower higher value for the following. How many cubic meters of water are in a cylindrical cumulus cloud of height 3km radius1km? How many 1L bottles would the water fill? Water has a density of 1000kg/m³ . How much mass does the water in the cloud have ? Do not link it to any other question and give me the final answer to this question only.