GEOMETRY QUESTIONS 2
1. Find the length of the diagonal of a cuboid 12m long, 9m broad, and 8 m high.
A. 18
B. 17
C. 20
D. 29
E. None of These
Correct Ans:17
Let l, b, and h be the length, breadth, and height of the cuboid respectively.
Diagonal of a cuboid= sqrt (l2 + b2 + h2)
= sqrt (12 2 + 92 + 82)
= sqrt (144+81+64)
= sqrt(289) = 17
Thus, Diagonal of the cuboid = 17 m
2. Sum of all external angles in any triangle is ______ degrees.
A. 180
B. 300
C. 540
D. 360
E. None of these
Correct Ans:360
3. Find the perimeter of the rectangle having length 24 cm and breadth 21 cm.
A. 504
B. 45
C. 95
D. 90
E. None of These
Correct Ans:90
Given length of the rectangle, l = 24 cm Breadth of the rectangle, b= 21 cm Perimeter of the rectangle is, P = 2(l+b) P = 2 x (24 + 21) cm P = 2 x 45 = 90 cm
4. Area of the base of a cuboid 49 sq m, area of side face and other side face are 64 sq m and 25 sq m respectively. Find the volume of the cuboid
A. 240
B. 260
C. 290
D. 280
E. None of These
Correct Ans:280
Let l, b and h be the length, breadth and height of the cuboid respectively. According to given data, Area of the base of a cuboid = l x b = 49 , ----> (1) Area of the one side face = b x h = 64 ------> (2) Area of the other side face = h x l = 25 -----> (3) On multiplying the above equations we get l x b x b x h x l x h = 49 x 64 x 25 => (l x b x h)^2 = 49 x 64 x 25 => l x b x h = 7 x 8 x 5 = 280 Volume of the cuboid = l x b x h = 280
5. Find the length of the diagonal of a cuboid 10m long, 8 m broad, and 5 m high.
A. 13.75
B. 14
C. 17
D. 23
D. None of These
Correct Ans:13.75
Let l, b, and h be the length, breadth, and height of the cuboid respectively.
Diagonal of cuboid = sqrt(lxl + bxb + hxh) = sqrt(10 x 10 + 5 x 5 + 8 x 8) = sqrt(100+25+64) Diagonal = sqrt(189) = 13.75
6. A tennis court has a length of 29 units, and breadth of 20 units. Find the area of the tennis court ?
A. 841
B. 49
C. 290
D. 580
E. None of These
Correct Ans:580
Area of Rectangle = length x breadth
29 x 20= 580
7. Find the volume of a cube of side 12 cm
A. 1788
B. 1728
C. 1628
D. 1718
E. None of these
Correct Ans:1728
Let the side of the cube be a Then, Volume of the cube V = a^3 = a x a x a V = 12 x 12 x 12 = 1728 cu cm
8. The circumference of a park is 750 m. A and B start walking from the same direction at 6.75 kmph and 4.75 kmph. At what time will they meet each other again?
A. 3 hours
B. 2.5 hours
C. 3.5 hours
D. 4 hours
E. None of These
Correct Ans:3 hours
Time taken by A to complete one revolution = 750/ (6.75 x 5)/18 sec = (750*18)/(6.75*5)sec.
Time taken by B = (750 x 18)/(4.75 x 5) sec
Time required = LCM of numerators / HCF of denominators = 750 x 1800 / 125 = 1800 x 6 seconds = (1800 x 6)/3600 hrs = 3 hours
9. Length and breadth of a rectangular plot is 20m & 27m respectively. Find the Difference between Area and Perimeter ?
A. 493
B. 352
C. 540
D. 446
E. None of These
Correct Ans:446
Difference between area & perimeter = (length x breadth ) - (2 x (length + breadth) ) = (20 * 27 ) - (2 * (20 + 27) ) = 540 - (2 * 47) = 540 - 94 = 446
10. Steve walks diagonally in a Square shaped park. Steve covers a distance of 10m. Can you find the perimeter of the Square park ?
A. 30 sqrt(2)
B. 20 sqrt(3)
C. 40 sqrt(2)
D. 20 sqrt(2)
E. None of These
Correct Ans:20 sqrt(2)
Given Steve walks distance of 10m
Park is in the shape of Square, so area of park (in shape of Square) = (Diagonal2) / 2
=> (102)/2 = 50sq.m
Side of the square is = sqrt(50) = 5 sqrt(2)
Perimeter = 4 x 5 sqrt(2) = 20 sqrt(2)
11. The area of rhombus is 256 square cm and one of its diagonal is twice the other in length. Then length of its larger diagonal is ?
A. 32 cm
B. 16 cm
C. 48 cm
D. 24 cm
E. None of These
Correct Ans:32 cm
Let diagonal of Rhombus be d1 = x
Second diagonal = d1 * 2 = 2x cm
Area of rhombus = 1/2 d1 .d2 =>1/2 d1 .d2 = 256 =>1/2 * x * 2x = 256 => x2 = 256 =>x = √256 = 16 cm
Larger diagonal = 2x =>2 X 16 = 32cm
12. Diameter of a roller is 2.4 m and it is 1.68 m long. If it takes 1000 complete revolutions once over to level a field, then the area of the field is ?
A. 12672 sq m
B. 12671 sq m
C. 12762 sq m
D. 1768 sq m
E. one of These
Correct Ans:12672 sq m
Given, Diameter of roller = 2.4 m => radius = 2.4 / 2 = 1.2 m
Circumference = 2Π x r = 2Π x1.2 m
Area covered in one revolution = 2.4 Π x 1.68 = 12.672 sq m ;
Total area of the field = 12.672 x 1000 = 12672 sq. m
13. If perimeter of a rectangle is 180 m and the difference between the length and the breadth is 8 metres, what is the area of the rectangle?
A. 2116 sq m
B. 2047 sq m
C. 2090 sq m
D. 2009 sq m
E. None of These
Correct Ans:2009 sq m
Let x = length of the rectangle and breadth = (x – 8) m
Given , perimeter of the rectangle = 180 m perimeter of the rectangle = 2 * (l+b) => 2(x + x - 8)= 180? => (2x - 8) = 90? =>2x = 90 + 8 = 98 => x = 49 m?
Breadth = 49 – 8 = 41 m
Area of the rectangle = l * b = 49 x 41 = 2009 sq. m
14. The side of a square is 2 cms less than the length of a rectangle and the breadth of the rectangle is 5 cms less than the side of the square. The area of the square is 324 sq. cms. What is the area of the rectangle?
A. 250 sq. cms
B. 260 sq. cms
C. 254 sq. cms
D. 258 sq. cms
E. None of These
Correct Ans:260 sq. cms
Side of a square = ?Area = ?324 = 18 cm
Length of the rectangle = 18 + 2 = 20 cm and breadth = 18 – 5 = 13 cm
Area of rectangle = Length x breadth = 20 x 13 = 260 sq. cm
A. 1220
B. 1200
C. 1250
D. 125
E. None of These
Correct Ans:1250
Sin 15° = sin (45° – 30°) = sin 45° x cos 30° – cos 45° x sin 30°
=1/√2 x √3/2 – 1/√2 x 1/2
= √3/2√2 – 1/2√2
= (√3 - 1) / 2√2
cos 15° = cos (45° – 30°) = cos 45°. cos 30° + sin 45°. sin 30°
= 1/√2 x√3/2 + 1/√2 x 1/2
=√3/2√2 + 1/2√2
= (√3+1)/2√2;
Let ABC be the right-angled triangle
AB = AC sin 15°
= (√3 – 1)/2√2 m
BC =AC cos 15° = (√3+1)/2√2 m
Area of ABC = 1/2 x AB x BC
= (1/2 x (√3 - 1)/ 2√2 x (√3+1)/ 2√2) sq m
= (3 - 1)/16 sq m
= 1/8 sq m
= 10000/8 cm
= 1250 sq cm
15. An equilateral triangle and a regular hexagon have equal perimeters. The ratio of the area of the triangle and that of the hexagon is ?
A. 1:1
B. 2:3
C. 3:2
D. 3:4
E. None of These
Correct Ans:2:3
Let x = side of triangle and y = side of regular hexagon
Given, 3x = 6y ? => x = 2y ?
Area of triangle = (?3/4) x^2
=> Area of hexagon = 6 X (?3/4) y^2 => 6 X (?3/4) * (x^2 /4) ----> Substituting y = x/2 => 3 (?3/8) x^2
=> Required ratio = (?3/4) x^2 : 3 (?3/8) x^2 = 2 : 3
16. An equilateral triangle and a regular hexagon have equal perimeters. The ratio of the area of the triangle and that of the hexagon is
A. (1 : 1)
B. (2 : 3)
C. (3 : 2)
D. (3 : 4)
E. None of These
Correct Ans:(2 : 3)
17. The four walls and ceiling of a room of length 25 ft., breadth 12 ft, and height 10 ft area to be painted. Painter A can Paint 200 sqr.ft in 5 days, painter B can paint 250 sqr.ft in 2 days. If A & B work together, in how many days do they finish the job?
A. 4 (11/32)
B. 9 (10/34)
C. 6 (10/33)
D. 7 (11/34)
E. 5 (12/32)
Correct Ans:6 (10/33)
Total area to be painted = 25*12 +2(10*12 + 10*25) = 1040 sqr.ft
A paints = 200/5 = 40 sqr.ft per day
B paints = 250/2 = 125 sqr.ft per day
A + B = 40 + 125 = 165 sqr.ft per day
Number of days = 1040/165 = 6 (10/33)
18. 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 516 m2. Find width of walkway ?
A. 1
B. 2
C. 3
D. 4
E. None of these
Correct Ans:3
Let the width of rectangle be x so the length & breath is increased by 2x
so new total area along with walkway is (60+2x)*(20+2x) so (60+2x) * (20+2x) - 60 * 20 = 516
=>(60+2x) * (20+2x) = 1716 =>(30+x) * (10+x) = 429 = 33*13
=>x = 3
19. The edge of a cuboid are in the ratio 1 : 2 : 3 and its surface area is 88 cm2. The volume of the cuboid is :
A. 24 cm3
B. 48 cm3
C. 64 cm3
D. 120 cm3
E. None of these
Correct Ans:48 cm3
Let the dimensions of the cuboid be x, 2x and 3x.
Then, Area of the cuboid = 2 (lb + bh + hl) = 2(x*2x + 2x*3x + x*3x) = 88
=> 2x2 + 6x2 + 3x2 = 44 => 11x2 = 44 => x2 = 4 => x = 2.
Therefore volume of the cuboid = l * b * h = (2*4*6) cm3 = 48 cm3.
20. 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?
A. 6
B. 26
C. 32
D. Data insufficient
E. None of these
Correct Ans:6
Sum of present dimension 48+30+52=130.
New dimension =156. Increase in dimension = 26.
Ratio of dimensions = 48:30:52 =>24:15:26
Therefore increase in the shortest side = 15*(26)/(24+15+26) = 6
21. A cone of height 9 cm with a diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm. The percentage of wood wasted is :
A. 25%
B. 30%
C. 50%
D. 75%
E. None of these
Correct Ans:75%
Volume of sphere = (4/3)πr3 = [((4/3)π*9*9*9)]cm3.
Volume of cone = (1/3)πr2 * h = [(1/3π)*9*9*9]cm3.
Volume of wood wasted = [((4/3π)*9*9*9) - ((1/3π)*9*9*9)]cm3
= (π*9*9*9)cm3.
Therefore required percentage = [((π*9*9*9)/((4/3π)*9*9*9))*100]%
= ((3/4)*100)%
= 75%.
22. The length of the side of a square is represented by x+2. The length of the side of an equilateral triangle is 2x. If the square and the equilateral triangle have equal perimeter, then the value of x is ________
A. 5
B. 14
C. 17
D. 4
E. None of these
Correct Ans:4
Since the side of the square is x + 2, its perimeter = 4 (x + 2) = 4x + 8
Since the side of the equilateral triangle is 2x, its perimeter = 3 * 2x = 6x
Also, the perimeters of both are equal. (i.e.) 4x + 8 = 6x (i.e.) 2x = 8 => x = 4
23. The circumference of a park is 750 m. A and B start walking from the same direction at 6.75 kmph and 4.75 kmph. In what time will they meet each other again ?
A. 3 hours
B. 2.5 hours
C. 3.5 hours
D. 4 hours
E. None of These
Correct Ans:3 hours
Time taken by A to complete one revolution = 750/ (6.75 x 5)/18 sec = (750×18)/(6.75×5)sec.
Time taken by B = (750 x 18)/(4.75 x 5) sec
Time required = LCM of numerators / HCF of denominators = 750 x 1800 / 125 = 1800 x 6 seconds = (1800 x 6)/3600 hrs = 3 hours
24. Find the volume of a cuboid with dimension 22 cm by 12 cm by 7.5 cm ?
A. 1960
B. 1880
C. 1980
D. 1970
E. None of these
Correct Ans:1980
Length of the cuboid be l, breadth of the cuboid be b, and height of the cuboid be h.
Volume of the cuboid is, V = l x b x h V = 22 x 12 x 7.5 = 1980 cu cm.
25. Find the volume of the cylinder which has a height of 14 meters and a base of radius 3 meters?
A. 396
B. 386
C. 406
D. 416
E. None of these
Correct Ans:396
Let r and h be the radius and height of the cylinders.
Volume, V = pi x r2 x h V = (22/7) x 3 x 3 x 14 = 22 x 9 x 2 = 44 x 9 V = 396 cu m
26. Find the volume of a cuboid with dimension 22 cm by 12 cm by 7.5 cm
A. 1960
B. 1880
C. 1980
D. 1970
E. None of these
Correct Ans:1980
Length of the cuboid be l, breadth of the cuboid be b and height of the cuboid be h.
Volume of the cuboid is, V = l x b x h V = 22 x 12 x 7.5 = 1980 cu cm.
27. A tennis court has a length of 29 units, and a breadth of 20 units. Find the area of the tennis court?
A. 841
B. 49
C. 290
D. 580
E. None of These
Correct Ans:580
Area of Rectangle = length x breadth
29 x 20= 580
28. Area of the base of a cuboid 49 sq m, area of side face, and other side face are 64 sq m and 25 sq m respectively. Find the volume of the cuboid
A. 240
B. 260
C. 290
D. 280
E. None of These
Correct Ans:280
Let l, b and h be the length, breadth and height of the cuboid respectively.
According to given data, Area of the base of a cuboid = l x b = 49 , ----> (1) Area of the one side face = b x h = 64 ------> (2) Area of the other side face = h x l = 25 -----> (3)
On multiplying the above equations we get l x b x b x h x l x h = 49 x 64 x 25 => (l x b x h)^2 = 49 x 64 x 25 => l x b x h = 7 x 8 x 5 = 280
Volume of the cuboid = l x b x h = 280
29. Find the curved surface area of a cylinder of length 7 m and a base of radius 4 meter
A. 196
B. 156
C. 166
D. 176
E. None of These
Correct Ans:176
Let r and h be the radius and height of the cylinder respectively.
r = 4 and h = 7
Curved Surface area , CSA = 2 x pi x r x h
= 2 x ( 22 / 7 ) x 4 x 7
= 176 sq m
30. A cone of height 9 cm with a diameter of its base 18 cm is carved out from a wooden solid sphere of radius 9 cm. The percentage of wood wasted is:
A. 25%
B. 30%
C. 50%
D. 75%
E. None of these
Correct Ans:75%
Volume of sphere = (4/3)πr3 = [((4/3)π*9*9*9)]cm3.
Volume of cone = (1/3)πr2 * h = [(1/3π)*9*9*9]cm3.
Volume of wood wasted = [((4/3π)*9*9*9)((
1/3π)*9*9*9)]cm3
= (π*9*9*9)cm3.
Therefore required percentage = [((π*9*9*9)/((4/3π)*9*9*9))*100]%
= ((3/4)*100)%
= 75%.
31. The ratio of the length and breadth of a plot is 4 : 3. If the breadth is 40 m less than the length, What is the perimeter of the plot?
A. 540
B. 560
C. 580
D. 520
E. None of these
Correct Ans:560
Let the length be 4x metres. Then, breadth = 3x metres. Then, 4x - 3x = 40 => x = 40 length l = (4 × 40) = 160 m breadth b = (3 × 40) = 120 m Perimeter = 2(160 + 120) = 2(280) = 560 m
32. If the radius of two circles are in the ratio 3 : 4 then the ratio of their areas, will be
A. 09:04
B. 03:04
C. 09:14
D. 09:16
E. None of these
Correct Ans:09:16
Let r1 and r2 be the radius of the circle. Ratio of the area = pi x r12 : pi x r22 = r12 : r22 = 3 x 3 : 4 x 4 = 9 : 16
33. Find the area between the two concentric circle of radius 30 and 20 units
A. 500pi
B. 400 pi
C. 300 pi
D. 200 pi
E. None of These
Correct Ans:500pi
34. A piece of wire when bent to form a circle will have a radius of 84 cm. If the wire is bent to form a square, the length of a side of the square is
A. 152 cm
B. 132 cm
C. 168 cm
D. 225 cm
E. None of These
Correct Ans:132 cm
Ans – B Length of the wire = Circumference of circle = 2?r => 2 x 22/7 x 84 = 528 cm
Perimeter of square = 528 cm =>4 x side = 528 cm =>Side =528/4 = 132 cm
35. The area of a circle is 2464 square metres. What will be its circumference?
A. 132 m
B. 176 m
C. 231 m
D. 272 m
E. None of These
Correct Ans:176 m
?r 2464? r = (2464 x 7) / 22 = 784 r = ?784 = 28 m ? Circumference = 2 ?r = 2 x 22/7×28 = 176 m
36. The length of the floor of a rectangular auditorium is 6 m more than the radius of a circle with a circumference of 572 m. The perimeter of the floor of the rectangular auditorium is 356 m. What will be the cost of flooring the auditorium (only the floor of the auditorium), if the cost of flooring is Rs 12/m?
A. Rs. 87,954
B. Rs. 91,236
C. Rs. 94,284
D. Rs. 75,490
E. None of These
Correct Ans:Rs. 94,284
Circumference of circle = 2?r => 572 = 2 x 22/7 x r => r =(572 x7)/2 x 22 = 91 =>Length of the floor = 91 + 6 = 97 m =>2(l+b) =356 ? 2 (97 + b) = 356 => 97 + b = 178 => B = 178 – 97 = 81 m => Area of the floor = 97 x 81 = 7857 sq. m => Required cost = 12 x 7857 = ?944284
37. One Side of a Rhombus measures 35 units. Can you find the Area of the Rhombus?
A. 70
B. 105
C. 140
D. 1225
E. None of these
Correct Ans:1225
Area = Side x Side = 35 * 35 = 1225
38. Find the curved surface area of a cylinder of length 7 m and a base of radius 3 meters.
A. 112
B. 122
C. 132
D. 182
E. None of These
Correct Ans:132
Let r and h be the radius and height of the cylinder respectively.
r = 3 and h = 7
Curved Surface area , CSA = 2 x pi x r x h CSA = 2 x (22/7) x 3 x 7 = 132 sq m
39. Find the perimeter of the rectangle having length 24 cm and breadth 21 cm.
A. 504
B. 45
C. 95
D. 90
E. None of These
Correct Ans:90
Given the length of the rectangle, l = 24 cm Breadth of the rectangle, b= 21 cm
Perimeter of the rectangle is, P = 2(l+b) P = 2 x (24 + 21) cm P = 2 x 45 = 90 cm
40. Area of the base of a cuboid 9 sq m, area of side face, and other side face are 16 sq m and 25 sq m respectively. Find the volume of the cuboid
A. 60
B. 120
C. 240
D. 360
E. None of These
Correct Ans:60
Let l, b and h be the length, breadth and height of the cuboid respectively.
Given, Area of the base of a cuboid = l x b = 9 , Area of the side face = b x h = 16 Area of the other side face = h x l = 25
On multiplying the above equations we get l x b x b x h x l x h = 9 x 16 x 25 (l x b x h)^2 = 9 x 16 x 25 l x b x h = 3 x 4 x 5 = 60
Volume of the cuboid = l x b x h = 60
41. Length and breadth of a rectangular plot is 25m & 34m respectively. Find the Difference between Area and Perimeter ?
A. 791
B. 614
C. 850
D. 732
E. None of These
Correct Ans:732
Difference between area & perimeter of rectangle = (length x breadth ) - (2 x (length + breadth) ) = (25 * 34 ) - (2 * (25 + 34)) = 850 - ( 2 * 59) = 850 - 118 = 732
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