Volume and Time

What is Volume?

In mathematics, Volume is defined as the three-dimensional space which is enclosed by an object. The Volume of an objectis expressed in the cubic unit such as cubic metre and cubic centimetre, cubic inch, cubic foot etc. Moreover, the SI unit of Volume is a metre cube (m³). For example, a cuboid is given with all its dimensions such as Length, breadth and height. Now, one has to find out the Volume of a rectangular prism using its dimension.

The volume of rectangular prism = Length x Breadth x Height

• 6 units x 2 units x 4 units
• 48 cubic units

There are various formulas to find out the Volume of the different object which is given below: –

What is Time?

Time is a term which is used in mathematics to identify the time solution, such as how much time is passed or how much time required. One can also say that time is a concept which shows the continuous sequence of events which occur in succession from past to present. The term time is expressed in seconds, minutes, hours, days, weeks, months and years. Moreover, the SI unit of time is Seconds.

The formula for calculation of time is given below: –

Time = Distance / Speed

Total number of hours in a day è24 hours

Total number of minutes in a day è

1 hour = 60 minutes

24 x 60 è 1440 minutes

Total number of seconds in a day è

1 minute = 60 seconds

1440 x 60 = 86400 seconds

The below table shows the Units of Time.

Quiz

1. Convert 45 minutes into hours?
2. 2/4 hour
3. ¼ hour
4. ¾ hour
5. 3 hour

Answer: -¾ hours, is the correct answer because

1-hour è 60 minutes

I minute = 1/60 hour

Therefore, 45 minutes = 45/60 = ¾ hour

2. Akash has his maths class at 4:00 PM every day. Now, if the class continuous for 25 minutes. Find out the time when maths class will exactly finish?
3. 4:25 PM
4. 4:20 PM
5. 4:10 PM
6. 4:15 PM

Answer: – 4:25 PM, is the correct answer because

The time of Akash maths class = 4:00 PM

The total duration of piano class = 25 minutes

Therefore, Total time at which the class finishes = Starting time of maths class + duration of maths class

Total time at which the class finishes = 4:00 + 0:25è4:25 PM

3. Find out the Volume ofthe cone if a right-angle triangle has sides 3 cm, 4 cm and 5 cm to form cone?
4. 14 π cm³
5. 10 π cm³
6. 12 π cm³
7. 16 π cm³

Answer: – 12 π cm³, is the correct answer because

Radius, r = 3 cm and h = 4 cm

 4 cm               5 cm

                   3 cm

therefore, Volume = 1/3 πr²h

• (1/3 π x 3² x 4) cm³
• 12 π cm³

4. A seminar hall has a width of 12 m and 15 m long. Now, if the total area of the ceiling and floor is equal to the total area of 4 walls, then find out the Volume of the hall?
5. 1000 m³
6. 1100 m³
7. 1200 m³
8. 1300 m³

Answer: -1200 m³, is the correct answer because

Then, 2(15 + 12) x h = 2(15 x 12)

h = 180/27è20/3m

therefore, Volume = (15 x 12 x 20/3) m³

• 1200 m³

5. There is a conical vessel full of water whose height is 24 cm and radius 5 cm. Now, from the conical vessel, the water is emptied in the cylindrical vessel with an internal radius of 10 cm. Find out the height of increased rise of water for the cylinder?
6. 2 cm
7. 4 cm
8. 6 cm
9. 8 cm

Answer: -2 cm, is the correct answer because

The total Volume of water in a conical vessel è 1/3 πr²h

• 1/3 π x 5² x 24

Let, “h” be the height of a cylindrical vessel.

Therefore, total volume of water in cylindrical vessel = πr²h

• π x 10² x h

The volume of water in vessel = volume of water in cylindrical vessel

• 1/3 π x 5² x 24 = π x 10² x h

h = 2 cm

6. If the radius of two spheres has a ratio of 4:7. Therefore, find out the ratio of their Volume?
7. 60:340
8. 64:340
9. 64:343
10. 60:343

Answer: -64:343, is the correct answer because

The radius of two spheres = 4:7

Therefore, volume ratio = 4³ : 7³

• 64: 343

7. Find out how many months in 1 year?
8. 24 months
9. 12 months
10. 18 months
11. 6 months

Answer: -12 months, is the correct answer because there are 12 months in 1 year.

8. In the table shown below, there are a different number of months in a different year.

Now, choose the best way to find out a total number of months in 8 years?

1. Subtract 12 from 8
2. Add 12 and 8
3. Multiply 8 by 12
4. Divide 12 by 8

Answer: -Multiply 8 by 12, is the correct answer as 8 x 12 è96 months in 8 years.

9. In clock which hand moves fastest?
10. Minute hand
11. Second hand
12. Hour hand
13. None of these

Answer: -Second Hand, is the correct answer because second hand make 1 revolution of the clock in 1 Minute, Minute hand make 1 revolution of the clock in 1 hour and hour hand make 1 revolution in 12 hours.

10. Find out how many cubes of 3 cm edge can be cut out from 18 cm cube edge?
11. 220
12. 216
13. 218
14. 214

Answer: -216, is the correct answer because

The Volume of cube = a³

Therefore, number of cubes = a³ / a³

• 18 x 18 x 18 / 3 x 3 x 3
• 5832 / 27 è216