Mensuration Mcqs - Set 2

1)   There are two circles of different radii. The area of a square is 196 sq.cm, whose side is half the radius of the larger circle. The radius of the smaller circle is three-seventh that of the larger circle. What is the circumference of the smaller circle ?

a. 12 π cm
b. 16 π cm
c. 24 π cm
d. 32 π cm
Answer  Explanation 

ANSWER: 24 π cm

Explanation:
Radius of larger circle

= 2×196−−−√=28cm

Circumference of smaller circle

= (37×28)cm=12cm

Circumference of smaller circle

= 2πr=2π×12= 24πcm


2)   The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?

a. 23.57 cm
b. 47.14 cm
c. 84.92 cm
d. 94.94 cm
Answer  Explanation 

ANSWER: 23.57 cm

Explanation:
Let the side of the square be a cm.

Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm
i.e. 4a = 60
A = 15
Diameter of the semicircle = 15 cm
Circimference of the semicircle
= 1/2(∏)(15)
= 1/2(22/7)(15) = 330/14 = 23.57 cm to two decimal places


3)   A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is__________?

a. 3.34
b. 2
c. 4.5
d. 5.5
Answer  Explanation 

ANSWER: 3.34

Explanation:
Area of the path = Area of the outer circle – Area of the inner circle = ∏{4/2 + 25/100}2 – ∏[4/2]2

= ∏[2.252 – 22] = ∏(0.25)(4.25) { (a2 – b2 = (a – b)(a + b) }
= (3.14)(1/4)(17/4) = 53.38/16 = 3.34 sq m


4)   The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles.

a. 4192 sq m
b. 4304 sq m
c. 4312 sq m
d. 4360 sq m
Answer  Explanation 

ANSWER: 4312 sq m

Explanation:
Let the radii of the smaller and the larger circles be s m and l m respectively.

2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 – ∏s2
= ∏{1762/∏2 – 1322/∏2}
= 1762/∏ – 1322/∏
= (176 – 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m


5)   The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square.

a. 200 sq cm
b. 72 sq cm
c. 162 sq cm
d. Cannot be determined
Answer  Explanation 

ANSWER: Cannot be determined

Explanation:
Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.

4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.


6)   The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square.

a. 18 : 5
b. 7 : 16
c. 5 : 14
d. None of these
Answer  Explanation 

ANSWER: None of these

Explanation:
Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.

a2 = 4096 = 212
a = (212)1/2 = 26 = 64
L = 2a and b = a – 24
b : l = a – 24 : 2a = 40 : 128 = 5 : 16


7)   A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?

a. 60 cm2
b. 30 cm2
c. 45 cm2
d. 15 cm2
Answer  Explanation 

ANSWER: 30 cm2

Explanation:
The circumference of the circle is equal to the permeter of the rectangle.

Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5
=> x = 1
Therefore l = 6 cm and b = 5 cm Area of the rectangle = 6 * 5 = 30 cm2


8)   The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?

a. 600 cm
b. 800 cm
c. 400 cm
d. 1000 cm
Answer  Explanation 

ANSWER: 800 cm

Explanation:
Area of the square = s * s = 5(125 * 64)

=> s = 25 * 8 = 200 cm
Perimeter of the square = 4 * 200 = 800 cm.


9)   What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?

a. Rs. 3944
b. Rs. 3828
c. Rs. 4176
d. None of these
Answer  Explanation 

ANSWER: None of these

Explanation:
Let the side of the square plot be a ft.

a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58 = Rs. 3944.


10)   An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?

a. Rs. 3642.40
b. Rs. 3868.80
c. Rs. 4216.20
d. Rs. 4082.40
Answer  Explanation 

ANSWER: Rs. 4082.40

Explanation:
Length of the first carpet = (1.44)(6) = 8.64 cm

Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 * 7) = 315 (13 – 0.04) = 4095 – 12.6 = Rs. 4082.40


11)   The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?

a. 27 m
b. 24 m
c. 18 m
d. 21 m
Answer  Explanation 

ANSWER: 18 m

Explanation:
Let the length and the breadth of the floor be l m and b m respectively.

l = b + 200% of b = l + 2b = 3b
Area of the floor = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l2 = 324 => l = 18.


12)   The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 867 sq m, then what is the breadth of the rectangular plot?

a. 8.5 m
b. 17 m
c. 34 m
d. 51 m
Answer  Explanation 

ANSWER: 17 m

Explanation:
Let the breadth of the plot be b m.

Length of the plot = 3 b m
(3b)(b) = 867
3b2 = 867
b2 = 289 = 172 (b > 0)
b = 17 m.


13)   The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?

a. 8
b. 12
c. 6
d. 2
Answer  Explanation 

ANSWER: 2

Explanation:
Let the sides of the rectangle be l and b respectively.

From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l – b = 8 – 6 = 2m.


14)   The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?

a. 1 : 96
b. 1 : 48
c. 1 : 84
d. 1 : 68
Answer  Explanation 

ANSWER: 1 : 96

Explanation:
Let the length and the breadth of the rectangle be 4x cm and 3x respectively.

(4x)(3x) = 6912
12×2 = 6912
x2 = 576 = 4 * 144 = 22 * 122 (x > 0)
=> x = 2 * 12 = 24
Ratio of the breadth and the areas = 3x : 12×2 = 1 : 4x = 1: 96.


15)   Find the area of a parallelogram with base 24 cm and height 16 cm.

a. 262 cm2
b. 384 cm2
c. 192 cm2
d. 131 cm2
Answer  Explanation 

ANSWER: 384 cm2

Explanation:
Area of a parallelogram = base * height = 24 * 16 = 384 cm2


16)   Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.

a. 225 cm2
b. 275 cm2
c. 285 cm2
d. 315 cm2
Answer  Explanation 

ANSWER: 285 cm2

Explanation:
Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2


17)   The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?

a. 25 cm2
b. 42 cm2
c. 49 cm2
d. None of these
Answer  Explanation 

ANSWER: None of these

Explanation:
Area of a triangle = r * s

Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 28/2 = 35 cm2


18)   If the sides of a triangle are 26 cm, 24 cm and 10 cm, what is its area?

a. 120 cm2
b. 130 cm2
c. 312 cm2
d. 315 cm2
Answer  Explanation 

ANSWER: 120 cm2

Explanation:
The triangle with sides 26 cm, 24 cm and 10 cm is right angled, where the hypotenuse is 26 cm.

Area of the triangle = 1/2 * 24 * 10 = 120 cm2


19)   What is the are of an equilateral triangle of side 16 cm?

a. 48√3 cm2
b. 128√3 cm2
c. 9.6√3 cm2
d. 64√3 cm2
Answer  Explanation 

ANSWER: 64√3 cm2

Explanation:
Area of an equilateral triangle = √3/4 S2

If S = 16, Area of triangle = √3/4 * 16 * 16 = 64√3 cm2;