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Home Questions & Answer Aptitude Questions & Answers Geometry Questions & Answers

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:
A5 : 4
B4 : 5

C3 : 5
DNone of these
Explanation:

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

Two cubes of thire sides ratio 2 : 3. Find its cube volumes ratio
A27 : 7
B27 : 8
C8 : 27

D8 : 25
Explanation:

a³ : b³ = 2³ : 3³
= 8 : 27

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
A216 Cm2
B256 Cm3
C216 Cm3

DNone of these
Explanation:

Volume of new cube = Sum of volume of three cubes

=3³+4³+5³

=216 cm³

The diagonal of a cube is 8√3. find its volume and surface area.
A34 Cm²
B364 Cm³
C384 Cm²
D384 Cm³

Explanation:

Let the edge of the cube be a.

so, the diagonal $\inline \fn_jvn \sqrt{3}a$ = 8√3

=> a=8

Surface area => 6 a2 => (6 × 8 × 8) Cm² => 384 Cm²

The surface area of a cube is 486 Cm³. Find its volume
A739 Cm³
B529 Cm³
C729 Cm³

DNone of these
Explanation:

Surface area of cube =6X (s)²

where "s" is the side of the cube

therefore,

6s²=486

hence, s²=81

=> s = 9 cm

theefore volume = (s)³ {as all the dimensions have same length}

=(9)³

^{=729 cm3}

The volume of cube is equal to the surface area of that cube. Then find the distance of side of the cube
A6 m

B7 m
C8 m
D9 m
Explanation:

Cube volume = a³ cubic units

Surface area = 6 a² sq. units

a³ = 6a²

a=6m

The lateral surface area of cube is 100 sq.units. find the volume of cube
A122 m3
B135 m3
C125 m3

D120 m3
Explanation:

Lateral surface area = 4a²=100 sq.units

So a2 = 100/4 = 25

∴a=25 and a = root of 25 which is = 5

So 5³ = 125 m³

The side of a cube is 15 m, find it's surface area
A1350 m2

B1250 m2
C1300 m2
D1450 m2
Explanation:

A=1350m²

The side of a cube is 8 m, Find the voiume
A513 m3
B514 m3
C512 m3

D502 m3
Explanation:

V=512m³

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
A395
B385
C415
D405

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
A98
B88

C99
D89
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

A rectangular parking space is marked out by painting three of its sides. If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, find out the area of the parking space in square feet
A126 sq. ft.

B128 sq. ft.
C136 sq. ft.
D116 sq. ft.
Explanation:

Let l = 9 ft.

Then l + 2b = 37

=> 2b = 37 – l = 37 – 9 = 28

b = 28/2 = 14 ft.

Area = lb = 9 × 14 = 126 sq. ft.

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
A20 metres

B25 metres
C27 metres
D18 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.
ARs. 25660
BRs. 25560
CRs. 25650

DRs. 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:
A17 cm
B17 m

C17 m2
D16 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:
A1:3
B3:1
C1:4
D4:1

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:
A350
B450

C460
D470
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
A46 cm
B48 cm
C46 m

DNone 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.
A120 m
B121 cm
C121 m

DNone 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:
A(5, 0)
B(-5, 0)
C(0, 5)
D(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:
A(4, 0)

B(0, 4)
C(4, 4)
D(-4, 4)
Explanation:

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

Find the distance of the point A(3, -3) from the origin.
A3√2

B3√6
C6√2
D7√2
Explanation:

OA = √32+(-3)2 = √9+9 = √18 = 3√2

Find the distance of the point A(4, -4) from the origin.
A3√2
B2√8
C6√2
D8√2

Explanation:

OA = √42+(-4)2 = √16+16 = √32 = 8√2

In which quadrant does the point(9, 0) lie
Ax-axis

By-axis
C4th
DNone of these
Explanation:

The point (9, 0) lies in y-axis.

In which quadrant does the point(0, 9) lie
Ax-axis
By-axis

C3rd
DNone of these
Explanation:

The point (0, 9) lies in x-axis.

In which quadrant does the point(-7, 6) lie
A1st
B2nd

C3rd
D4th
Explanation:

The point (-7, 6) lies in 2nd quadrant.

In which quadrant does the point(9, -2) lie
A1st
B2nd
C3rd
D4th

Explanation:

The point (9, -2) lies in 4th quadrant.

In which quadrant does the point(1, 5) lie
A1st

B2nd
C3rd
D4th
Explanation:

The point (1, 5) lies in 1st quadrant.

In which quadrant does the point(-4, -7) lie
A1st
B2nd
C3rd

D4th

If μ_r be the rth order centralmoment of a population μ₀ , μ₁ and μ₂ are : (where, σ = standard deviation)
A0, 1, σ²
B 1, 0, σ²

C1, 1, σ
D 1, 0, σ