Geometry Questions & Answers (Compiled from UPSC, SSC ,PSC ,IBPS previous question papers)

Two cubes of their volumes in the ratio 64 : 125. The ratio of their surface area is:
5 : 4
4 : 5
3 : 5
None of these
Explanation:

The ratio of their surface area is
64 : 125
4 : 5

Three cubes of sides 5 m, 4 m, and 3 m are melted to form a new cube. Find the surface of the new cube
216 Cm2
256 Cm3
216 Cm3
None of these
Explanation:

Volume of new cube = Sum of volume of three cubes

=3³+4³+5³

=216 cm³

The volume of cube is equal to the surface area of that cube. Then find the distance of side of the cube
6 m
7 m
8 m
9 m
Explanation:

Cube volume = a³ cubic units

Surface area = 6 a² sq. units

a³ = 6a²

a=6m

A large field of 900 hectares is divided into two parts. The difference of the areas of the two parts is one-fifth of the average of the two areas. What is the area of the smaller part in hectares
395
385
415
405
Explanation:

Let the areas of the two parts be x and (900-x) hectares

therefore, [x-(900-x)]=1/5[x+(900-x)/2]

=> 2x-900=90

=>x=495

Hence, area of smaller part = (900 - x) = (900 – 495) = 405 hectares.

A rectangular field has to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required
98
88
99
89
Explanation:

Area of the field $= 680$ sq. feet.

Length of the adjacent sides are
$20$ feet and $\frac{680}{20} = 34$ feet.

Required length of the fencing
$= 20 + 34 + 34 = 88$ feet

The area of a rectangle plot is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the plot
20 metres
25 metres
27 metres
18 metres
Explanation:

Let breadth=x meters.

Then,Length = $\frac{115x}{100}$ meters

Given that, $x\times \frac{115x}{100}=460$

=> x = 20

Breadth = 20

The length of a room is 6 m and width is 4.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 900 per sq. metre.
Rs. 25660
Rs. 25560
Rs. 25650
Rs. 26550
Explanation:

l=5.5m w=3.75m
area of the floor = 6 × 4.75 sq. metre.
cost of paving = 6 × 4.75 × 900 = 6 × 4275 = Rs. 25650

A rectangular mat has an area of 120 sq.metres and perimeter of 46 m. The length of its diagonal is:
17 cm
17 m
17 m2
16 m
Explanation:

Suppose, rectangular has lengtha and width b.
Then, an areaof rectangular equals:
(1) S = a*b =120 sq metres
and a perimeterequals:
P = 2a + 2b =46 metres
(2) a + b = P/2 =23
The length of itsdiagonal is:
l^2 = a^2 + b^2
But, a^2 + b^2 = (a + b)^2 - 2ab
Therefore:
l^2 = (P/2)^2 - 2S = 23^2 - 2*120 = 289
l = Sqrt[289] = 17 metres
Answer: The length of diagonal is 17 metres

The ratio of the areas of two squares, one having double its diagonal then the other is:
1:3
3:1
1:4
4:1
Explanation:

${\color{Black}ratio=\frac{\frac{1}{2}(2d)^{2}}{\frac{1}{2}d^{2}} =4:1 }$

A rectangular courtyard 3.78 m lang and 5.25 m broad is to be paved exactly with square tiles, all of the same size. The minimum number of such tiles is:
350
450
460
470
Explanation:

The length of courtyard = 3.78m = 378 cm

And, the broad of courtyard = 5.25m = 525cm

The courtyard is to be paved by square tiles of equal size.

∴ Size of square tile is the HCF of length and breadth as to cover exactly.

The HCF of 525 and 378 = 21 cm

Then, the side of each square tile = 21 cm

The number of tiles = 525×378/21×21

=450

A rectangle measures 8 Cm on length and its diagonal measures 17 Cm. What is the perimeter of the rectangle
46 cm
48 cm
46 m
None of these
Explanation:

Second side = √172-82
= √289-64
= 15 cm
Perimeter = 2 (l+b) = 2(8+5) Cm = 2(23) = 46 Cm

The sides of a rectangle are in the ratio of 6 : 5 and its area is 1331 sq.m. Find the perimeter of rectangle.
120 m
121 cm
121 m
None of these
Explanation:

Let 6x and 5x be sides of the rectangle
6x × 5x = 1331
11x2 = 1331
x2 = 1331/11 = 121 => x = 11
Length = 6x = 6 × 11 = 66
Breadth = 5x => 5 × 11 = 55
Perimeter = 2 (l+b) => 2 (66+55) = 121 m

A is a point on y-axis at a distance of 5 units from x-axis lying below x-axis. The co-ordinates of A are:
(5, 0)
(-5, 0)
(0, 5)
(0, -5)

P is a point on x-axis at a distance of 4 units from y-axis to its right. The co-ordinates of P are:
(4, 0)
(0, 4)
(4, 4)
(-4, 4)
Explanation:

The co-ordinates of P are A(4, 0)