Aptitude - Questions & Answers

Area Calculation - Online Quiz

Quiz

Following quiz provides Multiple Choice Questions (MCQs) related to Area Calculation. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using Show Answer button. You can use Next Quiz button to check new set of questions in the quiz.

Q 1 - A way of uniform width keeps running round within a rectangular Field 38m long and 32m wide. On the off chance that the way involves 600m², then The width of the way is:

Answer : B

Explanation

area of the field = (32*38)m²=  1216m²
Let the width of the path be x mtr.
Area without path= (38-2x) (32-2x) m²
= 1216+4x²-140x
Area of the path= 1216- (1216+4x²-140x) = 140x-4x²
∴ 140x-4x²=600
⇒4x²-140x+600=0
⇒x²-35x+150=0 ⇒ (x-30) (x-5) =0 ⇒x=5m

Q 2 - The biggest size of the bamboo can be set in a square of zone 100sq. meters is:

Answer : B

Explanation

side of the square = √100 m =10 m
Largest size of the bamboo= length of the diagonal of the square.
= √ (10) ²+ (10) ²m = √ 200m   = 10√ 2m
=(10*1.414) m 14.14m

Q 3 - If every side of a square is expanded by half, the proportion of the territory of the subsequent square to the range of the given square is:

Answer : B

Explanation

Let the original side be x mtr. Then, area =x² sq. mtr.
New side = (150% of x) m = (150/100* x) m = (3x/2) m
New area = (3x/2*3x/2) m²= 9x²/4 m²
Required ratio of areas = 9x²/4: x²= 9:4

Q 4 - Of the two square fields, the range of the one is 1 hectare, while another is more extensive by 1%. The distinction in ranges is:

Answer : B

Explanation

Area of one Sq. field= 10000m²
Side of this field = √10000m =100m
Side of another square = 101 m
Difference of area = [(101) ²-(100) ²] m²
=(101+100)(101-100)m2 = (201*1)m²= 201m²

Q 5 - The expense of setting up a four divider a room is Rs.480. Every one of the length, expansiveness and tallness of another room is twofold that of this room. The expense of setting up the dividers of new room is:

Answer : C

Explanation

Area of 4 walls of first room= [2(L+b)*h]
Area of 4 walls of another room = [2(2L+2b)*2h]
= 4*[2 (L+b)*h] = 4* original area
∴ required cost = (4*480) =1920 Rs.

Q 6 - The area of a square with side x is equal to area of a triangle with base x. the altitude of the triangle is:

Answer : C

Explanation

Let the altitude of the triangle be h. Then x²= 1/2*x*h ⇒h =2x
∴altitude = 2x

Q 7 - What is the proportion of the ranges of circles engraved and delineated in a square?

Answer : C

Explanation

Let, each side of the square be x. Then, its diagonal= √2x
Radius of in circle = x/2
Radius of circumcircle= √2x/2 = x/ √2
Required ratio = π(x/2)²: π(x/√2)² = πx²/4: πx²/2 = 2:4= 1:2

Q 8 - The range of a square is equivalent to the territory of a circle. What is the proportion between the side of the square and the span of the circle?

Answer : A

Explanation

Let the side of the square be a and radius of the circle be r.
       Then, a² =πr² ⇒a = √πr⇒ A/R=√π/1 ⇒a: r =√π:1

Q 9 - If the side of a square is expanded by 25%, then its region is expanded by:

Answer : D

Explanation

Let original side= a. Then , area =a²
New side= (125% of a) = (125/100*a) = 5a/4
New area = (5a/4* 5a/4) = (25/16) a²
Area increased = [(25/16)a²-a²] =9a²/16
Increased % = (9a²/16* 1/a²*100) %= 225/4= 56.25%

Q 10 - The region of a circle is 24.64m². The circuit of the circle is:

Answer : C

Explanation

πR²=24.64
⇒R²= (24.64*7/22)=(1.12*7)=7.84⇒R=√7.84=2.8
Circumference= 2πR= (2*22/7*2.8) m =17.60 m

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