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
cm

^{3}**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 A

^{2}and volume as A^{3}. Now A^{3}is given and you have to find A^{3}. How will you do it? Simple, first take the square-root of A^{2}to convert it into A, and then take the cube of A to find A^{3}.
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 A

^{2}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 A

^{2 }(or surface area) will increase by (1.5*1.5 – 1)*100 % = 125%*Note:*Similarly A

^{3 }(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 cm^{3}
Now this volume will be equal to the
volume of the sphere formed after melting the block

Volume of sphere = (4/3) * π * r

^{3}= 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 * r

^{3}= (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 * R

^{3}(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 * R

^{3}= (4/3) * π * r^{3}
r
: R = 1 : 2

^{2/3}
Surface
area of smaller sphere(s) = 4 * π * r

^{2}
Surface
area of larger sphere(S) = 4 * π * R

^{2}
S/s
= (r/R)

^{2}= 1 : 2^{4/3}**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 *
or

*l*, where*l*= slant height of the cone, which is
Hence
A = π*3*5 = 15π

B
= 2πrh = 2π*3*4 = 24π

C
= πr

^{2}= π*3^{2}= 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)

So,
OC/BC = OF/AB

OC
= 2 cm, therefore CG = 3 cm (OG = 1 cm)

Now,
ABC and CEG are similar

GE/AB
= CG/AC

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 :)**