Quick Method to Solve Mensuration Problems

How to Use this Trick

Check whether π=22/7 has been used in the formula for finding out the Particular Area, Curved Surface Area, Total Area, Volume, etc. If it is so, then

Here are examples to explain the chart given above.

Example 1:

Find the surface area of a sphere whose volume is 4851 cubic meters.

a) 1380 m2b) 1360 m2c) 1368 m2d) 1386 m2

Using the Trick:

We know that surface area of a sphere = 4πr2

It means ‘π’ has been used in finding out the surface area of the sphere.

We can easily see that only ‘1386’ from the given options is divisible by ‘11’

Hence, surface area of the sphere = 1386 m2

Example 2:

The radius and height of a right circular cylinder are 14 cm & 21 cm respectively. Find its volume.

a) 12836 cm3b) 12736 cm3c) 12936 cm3d) 12837 cm3

Using the Trick:

The know that volume of Cylinder = πr2h

We must check divisibility by ‘11’. Here, both ‘12936’ and ‘12837’ are divisible by 11. But you also notice that radius (14 cm) & height (21 cm) are both multiples of 7. So the option divisible by ‘7’ is your answer.

Hence, volume of a right circular cylinder = 12936 cm3 (since this is the only option divisible by 7)

We can test this as follows:

Volume of the given cylinder

= (22/7) × 14 × 14 × 14 × 21 cm3

= 22 × 14 × 14 × 3 cm3

⇒ Volume must be divisible by ‘7’.

Example 3:

The radius and height of a right circular cone are 7 cm & 18 cm respectively. Find its volume.

a) 814 cm3b) 624 cm3c) 825 cm3d) 924 cm3

Using the Trick:

The option should be divisible by ‘11’ because ‘π’ has been used in finding its volume. One of the parameters is a multiple of 7 without being a higher power. So we must go through fundamentals.

Now, volume of a right circular cone = (1/3)πr2h

= (1/3) × (22/7) × 7 × 7 × 18 cm3

= 22 × 7 × 6

Clearly, we need an answer that is a multiple of 11, 7 as well as 3.

Among the given options, 814, 825 and 924 are all multiples of 11. However, we see that only one option is divisible by 7. So this is the correct answer.

Hence, volume of the given cone = 924 cm3

Example 4:

Find the circumference of a circle whose radius is 49 cm.

a) 208 cm
b) 288 cm
c) 308 cm
d) 407 cm

Using the Trick:

The option should be divisible by ‘11’ because ‘π’ has been used in finding its circumference. One of the parameters is a higher power of 7. Thus, we need to find the only option that is a multiple of 7. If, however, we find more than one option that is a multiple of 7, we need to go through fundamentals.

Among the options, 308 and 407 are both multiples of 11. However, only 308 is a multiple of 7. So circumference of the circle = 308 cm.

We can test this as follows:

Circumference of circle = 2πr cm

= 2 × (22/7) × 7 × 49 cm

= 2 × 22 × 7 cm

Remember: If there is only one parameter equal to ‘7’ or multiple of ‘7’ and this parameter is not in a higher power in the formula, the answer will not be divisible by ‘7’

Example 5:

Find the curved surface area of a right circular cylinder whose radius & height are 14 cm & 50 cm respectively.

a) 3300 cm2b) 3420 cm2c) 4440 cm2d) 4400 cm2

Solution:

Curved surface area of a right circular cylinder = 2πrh

Here only one parameter (r = 14 cm) is a multiple of 7 (without being a higher power of 7). This parameter is used only as ‘r’ and not in its higher powers. So we see that our answer will not be a multiple of 7. However, the presence of π means that it will still be a multiple of 11.

Among the given options, 3300 and 4400 are both multiples of 11. We also see that both are not multiples of 7 either. However, we can see that none of our parameters are multiples of 3, so curved surface area cannot be a multiple of 3 either. So our answer cannot be 3300.

Therefore curved surface area of right circular cylinder must be 4400 cm2.

We can test this as follows:

Curved surface area of a right circular cylinder = 2πrh

=2 × (22/7) × 14 × 50

=2 × 22 × 2 × 50

= 4400 cm3

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