Competitive Exams : Quantitative Aptitude - Mensuration (2D/3D) (Set 2)

Question 1

A rectangular courtyard has a length of 24 mand width of18 m. A path of uniform width $x$is constructed inside along the boundary, reducing the area by$252m^2$.

Find the value of $x$(in meters).

Accepted Answer

A) 3

Answer

B) 2

Answer

C) 4

Answer

D) 2.5

Question 2

A solid metallic sphere of radius 6 cmis melted and recast into small cones, each of radius2 cmand height3 cm.

Calculate the number of cones formed.

Accepted Answer

B) 72

Answer

A) 64

Answer

C) 80

Answer

D) 54

Question 3

Two athletes start running in opposite directions on a circular track of length 1200 m. Speed of A is 18 km/hand B is27 km/h.

After how many seconds will they meet for the first time?

Accepted Answer

C) 96

Answer

A) 80

Answer

B) 100

Answer

D) 120

Question 4

If $x + \frac{1}{x} = \sqrt{3}$, what is the value of $x^{18} + x^{12} + x^6 + 1$?

Calculate the result.

Accepted Answer

A) 0

Answer

B) 1

Answer

C) 2

Answer

D) -1

Question 5

In a circle, chords ABandCDintersect internally at$P$. If $AP = 4$, $PB = 9$, and $CP = DP$, find CD.

Calculate the length of CD.

Accepted Answer

B) 12

Answer

A) 4

Answer

C) 6

Answer

D) 8

Question 6

The diagonal of a square is $12\sqrt{2}cm$. Find the area of the circle circumscribing this square.

Calculate the area (in $cm^2$).

Accepted Answer

D) $72\pi$

Answer

A) $64\pi$

Answer

B) $36\pi$

Answer

C) $100\pi$

Question 7

A cylindrical tank has a radius of 7 mand height of10 m. How many liters of water can it hold? (Take $\pi = 22/7$, $1m^3 = 1000 ext{ liters}$)

Calculate the capacity.

Accepted Answer

B) 1,540,000

Answer

A) 1,540,000

Answer

C) 770,000

Answer

D) 3,080,000

Question 8

The ratio of radii of two spheres is $3:4$. Find the ratio of their surface areas.

What is the surface area ratio?

Accepted Answer

A) 9:16

Answer

B) 27:64

Answer

C) 3:4

Answer

D) 1:2

Question 9

A wire is bent into a circle of radius 21 cm. If the same wire is bent into a square, what is the side of the square?

Find the side length (in cm).

Accepted Answer

C) 33

Answer

A) 22

Answer

B) 44

Answer

D) 66

Question 10

A cone of height 24 cmand base radius7 cmis submerged in a cylinder. Calculate the lateral surface area of the cone.

Find the LSA (in$cm^2$).

Accepted Answer

B) 550

Answer

A) 528

Answer

C) 500

Answer

D) 600

Question 11

The area of a rhombus is $150cm^2$. If one diagonal is 15 cm, find the length of the other diagonal.

Find the length of the other diagonal (in cm).

Accepted Answer

D) 20

Answer

A) 10

Answer

B) 25

Answer

C) 15

Question 12

A cuboid of dimensions $8cm imes 6cm imes 4cm$is melted. What is the side of a cube of equivalent volume?

Find the side length (in cm).

Accepted Answer

A) $\sqrt[3]{192}$

Answer

B) 8

Answer

C) 6

Answer

D) 4

Question 13

The volume of a sphere is $36\picm^3$. Find its total surface area.

Find the surface area (in $cm^2$).

Accepted Answer

C) $36\pi$

Answer

A) $16\pi$

Answer

B) $24\pi$

Answer

D) $48\pi$

Question 14

In an equilateral triangle of side $6\sqrt{3}$, find the radius of the incircle.

Find the radius (in cm).

Accepted Answer

B) 3

Answer

A) 2

Answer

C) 4

Answer

D) 6

Question 15

The length of a rectangular park is twice its width. Area is $800m^2$. Find the length.

Find the length (in m).

Accepted Answer

A) 40

Answer

B) 20

Answer

C) 60

Answer

D) 30

Question 16

A sector of a circle with central angle $60^\circ$has radius14 cm. Find the area of the sector.

Find the area (in $cm^2$).

Accepted Answer

D) 308/3

Answer

A) 308/3

Answer

B) 154/3

Answer

C) 308

Question 17

Calculate the diagonal of a cube with edge 4 cm.

Find the diagonal (in cm).

Accepted Answer

C) $4\sqrt{3}$

Answer

A) 4

Answer

B) $4\sqrt{2}$

Answer

D) 8

Question 18

Two circles touch externally. Their radii are 5 cmand3 cm. Find the distance between their centers.

Find the distance (in cm).

Accepted Answer

A) 8

Answer

B) 2

Answer

C) 4

Answer

D) 15

Question 19

Find the area of a triangle with sides 13 cm, 14 cm, and 15 cm.

Find the area (in $cm^2$).

Accepted Answer

B) 84

Answer

A) 74

Answer

C) 94

Answer

D) 64

Question 20

Find the total surface area of a hemisphere with radius 7 cm.

Find the TSA (in $cm^2$).

Accepted Answer

A) 462

Answer

B) 308

Answer

C) 154

Answer

D) 616

Set 3Competitive Exams : Quantitative Aptitude - Mensuration (2D/3D)