Sunday, 29 May 2016

[Q] Mensuration Tricks - 2

This is a famous question. Just remember whenever you are forming a circle and then a square,
the side of that square is given by, a = 1.6*r (approx.), where r = radius of the circle
I have written approx. because the actual formula is 1.57*r, but it will make the calculations a bit lengthy. So, just find 1.6*r and the answer will be little less than that. Like here
Side = 1.6*84 = 134.4, so the answer is 132 cm
Answer: (A)

When the wire is bent in the form of a circle of radius 84cm, that means the circumference (or the length of the wire) of the circle is 2*π*84 = 44*12 cm
Now this wire forms a square of (let’s say) side ‘a’
Then, 4a (perimeter of the square) = 44*12
Hence a = 132 cm

If the given rectangular sheet of paper (length =l, breadth = b) is rolled across its length to form a cylinder, having a height b, then volume of cylinder = (l*l*b)/4π
If rolled across its breadth, then = (b*b*l)/4π
In this question the sheet is rolled along its length, so volume = (l*l*b)/4π = 12*12*5/(4* π)
Volume = 180/ π cm3
Answer: (C)

In this question, the ratio of surface areas is given and they are asking the ratio of volumes. The word “sphere” is useless here. In such questions, just imagine area as A2 and volume as A3. Now A3 is given and you have to find A3. How will you do it? Simple, first take the square-root of A2 to convert it into A, and then take the cube of A to find A3.

So for solving this question, we just have to take the square-root of 4:9. The ratio will become 2:3. Then take the cube of 2:3. Hence the answer is 8:27
Answer: (C)

Here again ratio of areas is given, that means A2 is given, and we have to find A. So 4:9 will become 2:3
Answer: (A)

Diameter and perimeter are directly proportional, P = D*π, where P is the perimeter and D is the diameter.
Hence a 75% increase in diameter means a 75% increase in perimeter
 Answer: (D)

The area of base and the volume of a cone are directly proportional V = A * h/3, where V = volume and h = height of the cone
Hence a 100% increase in the area of the base would mean a 100% increase in the volume
Answer: (B)

A is increased by 50% hence A2 (or surface area) will increase by (1.5*1.5 – 1)*100 % = 125%
Note: Similarly A3 (or volume) will increase by (1.5*1.5*1.5 – 1)*100 % = 237.5%

Answer: (A)

Where ever the word “melting” is used in mensuration, it means only one thing – equate the volume
The volume of the rectangular block = l*b*h = 21*77*24 cm3
Now this volume will be equal to the volume of the sphere formed after melting the block
Volume of sphere = (4/3) * π * r3 = 21*77*24
Hence, r = 21 cm
Answer: (A)

The water rises by 5.6 cm. Take this 5.6 cm as the height of the cylindrical beaker and find its volume.
Volume of a cylinder = π*r*r*h = π * (7/2) * (7/2) * 5.6
Volume of the marbles (spherical in shape) = (4/3) * π * r3 = (4/3) * π * 0.7 * 0.7 * 0.7
No. of marbles dropped = Volume of beaker/Volume of a marble = 150
Answer: (B)

Let the radius of the big sphere be R.
Volume of a cone = (1/3) * π * R3 (since radius and volume are same as the radius of the sphere)
Let the radius of the smaller sphere = r
Then volume of cone = volume of smaller sphere
(1/3) * π * R3 = (4/3) * π * r3
r : R = 1 : 22/3
Surface area of smaller sphere(s) = 4 * π * r2
Surface area of larger sphere(S) = 4 * π * R2
S/s = (r/R)2 = 1 : 24/3
Answer: (D)

When a cone is hollowed out from a cylinder, we get the above figure
The whole surface area of the remaining solid = Area of A + Area of B + Area of C
A = curved surface area of the cone
B = curved surface area of the cylinder
C = area of the cylindrical base
A = π * r * l, where l = slant height of the cone, which is  or
Hence A = π*3*5 = 15π
B = 2πrh = 2π*3*4 = 24π
C = πr2 = π*32 = 9π
The whole surface area of the remaining solid = 15π + 24π + 9π = 48π
Answer: (C)

Given, AB = 3 cm, BC = 6 cm and OF = 1 cm
Height of the cone (AC) = √(6^2 - 3^2 ) = 3√3 cm
Triangles ABC and CFO are similar (RHS similarity)
OC = 2 cm, therefore CG = 3 cm (OG = 1 cm)
Now, ABC and CEG are similar
So, GE =
Required volume = Volume of cone (CDE) - Volume of Sphere
                                = 3π – (4/3)π
                                = (5/3)π

Answer: (C)

If you have any doubt in this article, please drop a comment.
Keep reading :)


  1. sir regularly post kijiye please.very eagerly waiting for ur tricks

  2. Bro,there is a doubt in the last question ,in the 3rd line.
    OC/BC=OF/AB, why BC is taken instead of AC. when it is applied 2nd time,similarity, it is understood by the way,i have taken AC in the 3rd line.
    Please explain, where i am lacking.

    Ur help is really admirable bro! Post atleast once in two days.

    1. When you apply similarity, match the sides opposite to the equal angles.
      In triangles ABC and CFO,
      ∠OFC = ∠ABC, the side opposite to ∠OFC is OC and the side opposite to ∠CAB is BC, hence we have written OC/BC

    2. Sir,
      Angle of OFC = Angle of BAC, right.

  3. This comment has been removed by the author.

  4. How did u get πr^2/2????
    Here triangle is not that case we do 3*60/360*πr^2=πr^2/2....
    Kindly explain...

    1. irrespective of the type of triangle, the grazed area will be given by πr^2. You can derive this by adding the area of sectors at the three vertices (replace a + b + c with 180)

  5. Its abt q.no2...

  6. You r Really helpful to the people like me..! If.possible please share hacks from LCM&HCF..

  7. Prashant regularly post karo if possible...gr8 blog..

  8. Prashant regularly post karo if possible...gr8 blog..

  9. Sir doubt,
    If the radius of right circular cylinder is decreased by 50% & height increased by 60%.then it's volume decreased by?

    1. you know the formula for the volume
      V = pie*r*r*h
      New volume = pie*(0.5r)*(0.5r)*(1.6h) = 0.4*pie*r*r*h = 0.4V
      So the volume is decreasing from V to 0.4V
      So there is 60% decrease

  10. sir in last ques vol of cone CDE 3*pie kaise aya?? pl explain sir..

  11. sir,oc=2 kese liya last question me??nd also 3 pie kese aya volume of CDE???

    1. Cylinder is divided in 2 parts that CG is 3
      I think

  12. In question no 12 why we are adding c.s.a of cylinder

  13. Quite amazing solutions, explained in easy manner.
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