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Mensuration

    Volume and Capacity

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8th class > Mensuration > Volume and Capacity

Volume and Capacity

Noth the terms "Volume" and "Capacity" are used interchageably. However, there isn't much of a difference between them.

(a) Volume is the amount of space occupied by an object while

(b) Capacity is the quantity of any substance that a container is capable of holding.

For example: If a water tin holds 100 cm3 of water then the capacity of that water tin is 100 cm3.

Note: Capacity is also measured in terms of litres (L).

The relation between litre and cm3 is:

1 mL = 1 cm3

1 L = 1000 cm3

Therefore,

1 m3 = 1000000 cm3 = 1000 L

Let's Solve

Instructions

Equation blanks: Upon clicking on the blank, you will be provided with a variety of algebraic operations. Use these operations to enter the appropriate answer. For example: To enter perimeter of rectangle, 2(l + b), we need to put '2x(l+b)'. Make sure to use the bracket to be clear about the entities that are getting operated on.

  • Given a cylindrical tank, in which situation do we need to find the surface area and which situation concerns the volume:
To find how much water it can hold
Number of cement bags required to plaster it
To find the number of smaller tanks that can be filled with water from it
Volume
Surface Area
Neither

Solution:

(a) The more space a tank has within it, the more water it will hold. Since, this situation pertains to the space occupied by the tank, we need to evaluate the volume.

(b) The plastering is done on the surface of an object. Since, this is regarding the surface of the container, we will work with the the surface area of the tank.

(c) Similar to (a), the more amount of water that it can hold, the more smaller cans will be filled. Since, this is about the holding capacity of the tank, we find work with volume.

A rectangular paper of width 14 cm is rolled along its width and a cylinder of radius 20 cm is formed. The volume of the formed cylinder is:

Paper rolled into cylinder

  • From the question, we know that the height of the cylinder = cm
  • Putting, the values of r and h into the volume formula, we get volume = cm3
  • Substituting values
  • Volume of formed cylinder has been found.

A milk tank is in the form of cylinder whose radius is 1.5 m and length is 7 m. The quantity of milk in litres that can be stored in the tank is:

Volume of tank = πxr2xh

  • Putting the values in the volume formula.
  • We get volume = m3
  • The capacity of the tank becomes L
  • Capacity of the tank has been found.

A godown is in the form of a cuboid of measures 60 m × 40 m × 30 m. The number of cuboidal boxes that can be stored in it, if the volume of one box is 0.8 m3 is:

Volume of the godown = lxbxh

  • Putting the values in the volume formula.
  • We get volume of godown = m3
  • Next, the volume of a single box has been given as m3
  • Thus, the number of boxes that can be kept in the godown is equal to
  • Number of boxes that can be stored has been found.

Water is pouring into a cubiodal reservoir at the rate of 60 litres per minute. If the volume of reservoir is 108 m3, the number of hours it will take to fill the reservoir is:

First, find the rate of water flow

  • Since, 1 L = m3, the rate of water flow = L/min (given) = m3min
  • Further, the rate of water flow per hour = m3hr
  • Now, using the unitary method, we know that 1 m3 will get filled in hours.(Enter number upto two decimal places)
  • Thus, the number of hours taken to fill the reservoir: hours (Round up the result to the nearest whole number)
  • Time taken to fill reservoir has been found.