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# Area Questions

Home > Quantitative Aptitude > Area > General Questions
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The dimensions of a certain machine are 48" X 30" X 52". If the size of the machine is increased proportionately until the sum of its dimensions equals 156", what will be the increase in the shortest side?

A10"

B8"

C6"

D8.5"

Explanation:

48+30+52=130, then 156-130=26

the "proportionately" in the shortest side means 30/130*26=6"

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A square and an equilateral triangle have the same perimeter. What is the ratio of the area of the circle circumscribing the square to the area of the circle inscribed in the triangle?

A9:32

B8:27

C32:09:00

D27:08:00

Explanation:

let x be side of square
perimeter of square=4x=perimeter of triangle=3*side of triangle
so side of eq. triangle=(4/3)*x
diameter of circle circumscribing the square=sqrt(2)*x
area of circle circumscribing the square=pi*(sqrt(2)*x)^2/4=(pi/2)*x^2 ----(1)
to find radius of the circle inscribed in the triangle
area of triangle=r*s=sqrt(3)/4 * (4x/3)^2
now s=(4/3)*x+(4/3)*x+(4/3)*x/2=2x
so sqrt(3)/4 * (4x/3)^2=r*2x gives
r={2/3*(3^1/2)}*x
area of the circle inscribed in the triangle=pi*({2/3*(3^1/2)}*x)^2
=pi*(4/27)*x^2 -------(2)
so reqd ratio= eqn(1)/eqn(2)
=((pi/2)*x^2)/(pi*(4/27)*x^2)=27/8
so reqd ratio=27:8

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There is a rectangular Garden whose length and width is 60m X 20m.There is a walkway of uniform width around garden. Area of walkway is 516m^2. Find width of walkway?

A6

B3

C4

D2

Explanation:

Lets assume width of rectangle = x m.
So new length will be (60+2x) and width (20+2x)
Area of walkway = 516m^2
=> (60+2x)*(20+2x)-(60*20)=516.
=> (60+2x)*(20+2x)=1716.
=> (30+x)*(10+x)=429
=> x=3m

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A store owner is packing small radios into larger boxes that measure 25 in. by 42 in. by 60 in. If the measurement of each radio is 7 in. by 6 in. by 5 in., then how many radios can be placed in the box?

A300

B400

C420

D480

Explanation:

No of radios that can be placed in the box = (25*42*60)/(7*6*5)=300

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Two circles touch each other externally. The distance between their centres is 14 cm and the sum of their areas is 130 cm^2. Find their radii.

A9, 5

B13, 1

C11,3

D10,4

Explanation:

Lets assume the radius of 1st circle = x cm.
so, the radius of 2nd circle = (14-x)cm.

(pi*x*x)+(pi*(14-x)*(14-x))=130
By solving above eq.
x = 11 or 3

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If the radius of a circle is increased by 20% then the area is increased by:

A44%

B120%

C144%

D40%

Explanation:

Let say radius = ?r^2 = ?10^2 = 100?
New radius = 10 * 120% = 12
New area = ?12^2 = 144?
Increment = [(144??100?)/100?]*100 = 44%

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A photograph is to be fitted in a photo frame of sides 18 cm by 15 cm such that there is a margin of 1.5 cm left. What should be the area of the photograph?

A140 cm2

B180 cm2

C270 cm2

DNone of these

Explanation:

Given, 1.5 cm margin on bothsides.
So side will be increase by 1.5+1.5 = 3cm
Area of photograph = (18-3) * (15-3)
=180 cm^2

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