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Area Questions

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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

Answer: Option C

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%

Answer: Option A

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 closed wooden box of thickness 0.5 cm and length 21 cm, width 11 cm, and height 6 cm, is painted on the inside. The cost of painting is Rs 70. What is the rate of painting in rupees per sq. cm?


A0.7

B0.5

C0.1

D0.2

Answer: Option A

Explanation:

Since the box is thick of 0.5cm then we will have to find the inner dimensions of the box which is painted.



Length= 21-0.5*2=20, Width= 11-0.5*2=10 , Height= 6-0.5*2= 5



Total surface area:= 20*10*5=1000cm2



1000cm2 costs 70rs then cost per square cm will be 0.07Rs.

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In triangle PQR, PQ=6 cm,PR=8 cm and QR=12 cm. Calculate the area of the triangle PQR:


A17.5 cm^2

B23.33 cm^2

C28.67 cm^2

D21.33 cm^2

Answer: Option D

Explanation:

s=6+8+12/2=26/2=13
area=sqrt(s(s-a)(s-b)(s-c)
sqrt(13(13-6)*(13-8)*(13-12))
sqrt(455)=21.33 cm^2

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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

Answer: Option B

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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If the area of a square region having sides of length 6 cms is equal to the area of a rectangular region having width 2.5 cms, then the length of the rectangle, in cms, is


A14.4 cms.

B14 cms.

C15.4 cms.

DNone of these

Answer: Option A

Explanation:

Given:
Area of the square = Area of rectangle
square side length = 6 cms. And rectangle width = 2.5 cms.

6^2 = l*2.5
l = 14.4 cms.

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A closed cylindrical tank contains 36 ? cubic feet of water and its filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?


A3 feet.

B3.5 feet

C6 feet.

D7 feet.

Answer: Option A

Explanation:

Formula to get volume of cylinder = πr^2h

Given height of tank = 4ft.

=> πr^2 * 4 = 36π

=> r = 3

=> cylinder diameter = 6 feet.





When the tank is placed on its side on level ground.

The height of the surface of the water above the ground = 3 feet.

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The perimeter of a equilateral triangle and regular hexagon are equal. Find out the ratio of their areas?


A3:2

B2:3

C1:6

D6:1

Answer: Option B

Explanation:

Perimeter of equilateral triangle = Perimeter of regular hexagon
6r=3a => a/r=2
(sqrt(3)/4)a^2:3sqrt(3)/2 r^2
=>a^2/r^2:3*2 =4:6=2:3

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17 X 8 m rectangular ground is surrounded by 1.5 m width path. Depth of the path is 12 cm. Gravel is filled and find the quantity of gravel required.


A5.5 m^3

B7.5 m^3

C6.5 m^3

D10.08 m^3

Answer: Option D

Explanation:

Area of the rectangular ground = 17*8=136 m^2

Area of the big rectangle considering the path width = (17+2*1.5)*(8+2*1.5) = 220 m^2





Area of the path = 220−136 = 84 m^2

Gravel required = 84 m^2 * 12/100 m = 10.08 m^3

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The sticks of the same length are used to form a triangle as shown below. If 87 such sticks are used then how many triangles can be formed?


tcs-mock-test-sticks-of-same-length-are-used-to-form-a-triangle

A44

B43

C34

D45

Answer: Option B

Explanation:

First triangle is formed by using 3 sticks, but any subsequent triangle may be formed by using 2 sticks.

Therefore, If 1st triangles uses 3 sticks,



Remaining sticks = 87 - 3 = 84.  With these 84, we can form 42 triangles. So total = 42 + 1 = 43

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