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Mensuration - MCQ 5 - Banking Exams MCQ


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20 Questions MCQ Test Quantitative Aptitude for Competitive Examinations - Mensuration - MCQ 5

Mensuration - MCQ 5 for Banking Exams 2024 is part of Quantitative Aptitude for Competitive Examinations preparation. The Mensuration - MCQ 5 questions and answers have been prepared according to the Banking Exams exam syllabus.The Mensuration - MCQ 5 MCQs are made for Banking Exams 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Mensuration - MCQ 5 below.
Solutions of Mensuration - MCQ 5 questions in English are available as part of our Quantitative Aptitude for Competitive Examinations for Banking Exams & Mensuration - MCQ 5 solutions in Hindi for Quantitative Aptitude for Competitive Examinations course. Download more important topics, notes, lectures and mock test series for Banking Exams Exam by signing up for free. Attempt Mensuration - MCQ 5 | 20 questions in 15 minutes | Mock test for Banking Exams preparation | Free important questions MCQ to study Quantitative Aptitude for Competitive Examinations for Banking Exams Exam | Download free PDF with solutions
Mensuration - MCQ 5 - Question 1
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A slice from a circular pizza of diameter 14 inches is cut in a such a way that each slice of pizza has a central angle of 45°. What is the area of each slice of Pizza(in square inches)?

Detailed Solution for Mensuration - MCQ 5 - Question 1

D = 14
R = D/2 = 14/2 =7
Area of each slice of Pizza =πr² * Θ/360°
= (22/7) * 7 * 7 * (45°/360°)
=19.25

Mensuration - MCQ 5 - Question 2
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A rectangular courtyard 3.78 m long and 5.25 m broad is to be paved exactly with square tiles, all of the same size. What will be the minimum number of such tiles is?

Detailed Solution for Mensuration - MCQ 5 - Question 2

378 = 2 * 3 * 3 * 3 * 7
525 = 3 * 5 * 5 * 7
Highest Common Factor(HCF) = 3 * 7 = 21
Size of largest tile = 0.21 m by 0.21 m
Minimum Number of tiles = (3.78 * 5.25) / (0.21 * 0.21) = 450

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Mensuration - MCQ 5 - Question 3
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Circumference of a circle A is 22/7 times perimeter of a square. Area of the square is 784 cm². What is the area of another circle B whose diameter is half the radius of the circle A(in cm²)?

Detailed Solution for Mensuration - MCQ 5 - Question 3

Area = 784 cm²
a = 28 cm
Perimeter of Square = 4 * 28
Circumference of a Circle = 4 * 28 * 22/7
2πr = 4 * 4 * 22
r = 16 * 22 * 7 / 2 * 22 = 56 cm Radius of Circle B = 56/4 = 14 cm Area of Circle = πr² = 22/7 * 14 * 14 = 616 cm²

Mensuration - MCQ 5 - Question 4
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The area of a rectangle is equal to the area of a square whose diagonal is 12√6 metre. The difference between the length and the breadth of the rectangle is 6 metre. What is the perimeter of rectangle ? (in metre).
Detailed Solution for Mensuration - MCQ 5 - Question 4

d = a√2
12√6 = a√2
a = 12√3 l * b = a² = (12√3)² = 432
l – b = 6 ; l = b + 6
(b + 6)*(b) = 432
b² + 6b – 432 = 0
b = 18; l = 24
2(l + b) = 2(24 + 18) = 84m

Mensuration - MCQ 5 - Question 5
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The area of a rectangle gets reduced by 9 square units,if its length is reduced by 5 units and breadth is increased by 3 units.If we increase the length by 3 units and breadth by 2 units, then the area is increased by 67 square units. Find the length and breadth of the rectangle.
Detailed Solution for Mensuration - MCQ 5 - Question 5

Length = x; Breadth =y
xy – (x-5)(y+3) = 9
3x – 5y – 6 = 0 —(i)
(x+3)(y+2) – xy = 67
2x + 3y -61 = 0 —(ii)
solving (i) and (ii)
x = 17m ; y = 9m

Mensuration - MCQ 5 - Question 6
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Height of a cylindrical jar is decreased by 36%. By what percent must the radius be increased, so that there is no change in its volume?
Detailed Solution for Mensuration - MCQ 5 - Question 6

volume of cylindrical jar = πr1²h
volume of cylindrical jar = πr2²(64/100)*h = (16/25)*πr2²h
r2²/r1² = 25/16
r2 /r1 = 5/4
(r2 – r1)/r1 = (5 – 4)/4 * 100 = 25%

Mensuration - MCQ 5 - Question 7
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The sum of the radius and height of a cylinder is 19m. The total surface area of the cylinder is 1672 m², what is the volume of the cylinder?(in m³)
Detailed Solution for Mensuration - MCQ 5 - Question 7

r + h = 19 m
2πr(r + h) = 1672
r = 1672 * 7/ 2 * 22 * 19 = 14
r = 14 ; h = 5
volume of the cylinder = πr²h = (22/7) * 14 * 14 * 5 = 3080 m³

Mensuration - MCQ 5 - Question 8
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If the length of a rectangular field is increased by 20% and the breadth is reduced by 20%, the area of the rectangle will be 192m². What is the area of original rectangle?
Detailed Solution for Mensuration - MCQ 5 - Question 8

length of rectangle = l m
breadth of rectangle = b m
l * (120/100) * b * (80/100) = 192
1.2l * 0.8b = 192
lb = 192 / 1.2 * 0.8 = 200 m²

Mensuration - MCQ 5 - Question 9
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The respective ratio of curved surface area and total surface area of a cylinder is 4:5. If the curved surface area of the cylinder is 1232cm², What is the height?
Detailed Solution for Mensuration - MCQ 5 - Question 9

4x = curved surface area = 1232
x = 308
5x = total surface area = 1540
curved surface area = 2πrh
total surface area = 2πr(r + h)
2πr(r + h) = 1540
2πr² + 2πrh = 1540
2πr² = 1540 – 1232
r = 7; h = 28

Mensuration - MCQ 5 - Question 10
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The perimeter of a square is equal to twice the perimeter of a rectangle of length 8 cm and breadth 7 cm. What is the circumference of a semicircle whose diameter is equal to the side of the square ?
Detailed Solution for Mensuration - MCQ 5 - Question 10

Perimeter of square = 2 x Perimeter of rectangle
= 2 * 2 (8+7) = 60 cm.
Side of square = 60/4 = 15 cm = Diameter of semi-circle
Circumference of semi-circle = πd/2 + d
= (22/7) * 2 * 15 + 15 = 38.57 cm

Mensuration - MCQ 5 - Question 11
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Perimeter of a square and an equilateral triangle is equal. If the diagonal of the square is 10√2 cm, then find the area of equilateral triangle?
Detailed Solution for Mensuration - MCQ 5 - Question 11

Diagonal of a square = a√2 = 10√2
so a = 10, perimeter of square = 4*10 = 40 = 3x (x is the length of each side of triangle)
x = 40/3, so are of equilateral triangle = √3/4*40/3*40/3 = (400√3)/9 cm2

Mensuration - MCQ 5 - Question 12
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Length of a rectangular field is increased by 10 meters and breadth is decreased by 4 meters, area of the field remains unchanged. If the length decreased by 5 meters and breadth is increased by 7 meters, again the area remains unchanged. Find the length and breadth of the rectangular field.
Detailed Solution for Mensuration - MCQ 5 - Question 12

Length = l and breadth = b,
(l +10)*(b-4) = lb and (l-5)*(b+7) = lb
Solve both equation to get l and b

Mensuration - MCQ 5 - Question 13
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If the length of the rectangle is increased by 20%, by what percent should the width be reduced to maintain the same area?
Detailed Solution for Mensuration - MCQ 5 - Question 13

let length = 100 and breadth = 100
now new length = 120 and let breadth = b
so, 100*100 = 120*b
b = 250/3, so % decrease = 100 – 250/3 = 50/3 = 16.67%

Mensuration - MCQ 5 - Question 14
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A cone whose height is half of its radius is melted to from a hemi-sphere. Find the ratio of the radius of the hemi-sphere to that of cone.
Detailed Solution for Mensuration - MCQ 5 - Question 14

volume will remains constant. So,
V = 1/3*22/7*r2*r/2 (volume of cone) and V = 2/3*22/7*R3 (volume of hemisphere)
So, R/r = 1:4

Mensuration - MCQ 5 - Question 15
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Find the number of spherical balls of radius 1 cm that can be made from a cylinder of height 8 cm and diameter 14 cm?
Detailed Solution for Mensuration - MCQ 5 - Question 15

(22/7)*7*7*8 = x*(4/3)*(22/7)*13 (x = number of spherical balls)

Mensuration - MCQ 5 - Question 16
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A rectangle whose sides are in the ratio 6:5 is formed by bending a circular wire of radius 21cm. Find the difference between the length and breadth of the rectangle?
Detailed Solution for Mensuration - MCQ 5 - Question 16

circumference of the wire = 2*(22/7)*21 = 22*6
perimeter of rectangle = 2*11x = 22*6, so x= 6
difference = 36 -30 = 6cm

Mensuration - MCQ 5 - Question 17
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A right circular cone is exactly fitted inside a cube in such a way that the edges of the base of the cone are touching the edges of one face of the cube and the vertex is on the opposite face of the cube. If the volume of the cube is 512 cubic cm. find the approximate volume of the cone?
Detailed Solution for Mensuration - MCQ 5 - Question 17

when cone is completely fitted inside the cube, then diameter of cone = side of cube and height of cone = height of cube
so, volume = (1/3)*(22/7)*4*4*8 = 134 (approx)

Mensuration - MCQ 5 - Question 18
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if the radius of a cylinder is doubled and height is halved, what is the ratio between the new volume and the previous volume?
Detailed Solution for Mensuration - MCQ 5 - Question 18

New volume = (22/7)*4r2*h/2 and old volume = (22/7)*r2*h
so ratio = 2:1

Mensuration - MCQ 5 - Question 19
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A cone of radius 12 cm and height 5 cm is mounted on a cylinder of radius 12 cm and height 19 cm. Find the total surface area of the figure thus formed?
Detailed Solution for Mensuration - MCQ 5 - Question 19

total surface area = curved surface area of cone + curved surface area of cylinder + base area
= (22/7)*12*13 + (22/7)*12*19 + (22/7)*12*12 = 2376 cm2

Mensuration - MCQ 5 - Question 20
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A rectangular garden is 30 meter long and 20 meter broad. It has 6 meter wide pavements all around it both on its inside and outside. Find the total area of pavements?
Detailed Solution for Mensuration - MCQ 5 - Question 20

Required area = 42*32 – 18*8 = 1200

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