Quantitative Aptitude
Mensuration
2,507 Questions
Mensuration Questions
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$\displaystyle 2,464cm$
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$\displaystyle 2,404{ cm }^{ 3 }$
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$\displaystyle 2,444{ cm }^{ 3 }$
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$\displaystyle 2,464{ cm }^{ 3 }$
D
Correct answer
Explanation
Volume of a cone = (1/3)pi*r^2*h = (1/3)(22/7)14*14*12 = (1/3)(22/7)*196*12 = 22*28*4 = 2464.
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$\displaystyle 8600{ cm }^{ 2 }$
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$\displaystyle 8800{ cm }^{ 3 }$
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$\displaystyle 7800{ m }^{ 3 }$
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$\displaystyle 9800{ cm }^{ 9 }$
B
Correct answer
Explanation
Volume of a cone = (1/3) * pi * r^2 * h. Given r = 20, h = 21, pi = 22/7. Volume = (1/3) * (22/7) * 20^2 * 21 = (1/3) * 22 * 400 * 3 = 8800 cm^3.
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$6.2$ ft
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$6.0$ ft
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$5.2$ ft
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$6.4$ ft
D
Correct answer
Explanation
Volume of a cone = (1/3) * pi * r^2 * h. 440 = (1/3) * (22/7) * r^2 * 10. 440 * 3 * 7 / (22 * 10) = r^2. 44 * 21 / 22 = r^2. 2 * 21 = r^2. 42 = r^2. r = sqrt(42) which is approx 6.48.
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$0.170$ m
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$1.170$ m
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$0.290$ m
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$0.270$ m
A
Correct answer
Explanation
The volume of the submerged solid is 12 * 14 * 10 = 1680 m^3. This volume equals the volume of the water displaced in the cylindrical container: pi * r^2 * h_rise. So, 1680 = (22/7) * 56^2 * h_rise. h_rise = 1680 / (22 * 8 * 56) = 1680 / 9856 = 0.1704 m.
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$\displaystyle 36\pi { \ cm }^{ 3 }$
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$\displaystyle 36\pi\ cm$
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$\displaystyle 36\pi { \ m }^{ 3 }$
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$\displaystyle 26\pi {\ cm }^{ 3 }$
A
Correct answer
Explanation
Volume of sphere = (4/3) * pi * r^3. With r=3, V = (4/3) * pi * 27 = 36 * pi.
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$\displaystyle 7134.56{\ m }^{ 3 }$
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$\displaystyle 7234.56{\ m }^{ 3 }$
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$\displaystyle 7034.56{ \ m }^{ 3 }$
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$\displaystyle 7334.56{ \ m }^{ 3 }$
B
Correct answer
Explanation
Volume of sphere = 4/3 * pi * r^3. With r = 12, V = 4/3 * 3.14159 * 1728 = 7238.23. The closest option provided is 7234.56.
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$\displaystyle 112.66{ \ cm }^{ 3 }$
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$\displaystyle 718.66{\ cm }^{ 3 }$
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$\displaystyle 12.66{ \ cm }^{ 3 }$
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$\displaystyle 132.66{ \ cm }^{ 3 }$
B
Correct answer
Explanation
Volume of a hemisphere = (2/3) * pi * r^3. Volume = (2/3) * (22/7) * 7^3 = (2/3) * 22 * 49 = 2156 / 3 = 718.666... cm^3.
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$\displaystyle V=6234.56{\ ft }^{ 3 }$ and $ A=1808.64{\ ft }^{ 2 }$
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$\displaystyle V=7234.56{ \ ft }^{ 3 }$ and $ A=1808.64{\ ft }^{ 2 }$
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$\displaystyle V=6234.56{ \ ft }^{ 3 }$ and $ A=2808.64{ \ ft }^{ 2 }$
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$\displaystyle V=7134.56{\ ft }^{ 3 }$ and $ A=1808.64{ \ ft }^{ 2 }$
B
Correct answer
Explanation
The volume of a sphere is (4/3) * pi * r^3 and the surface area is 4 * pi * r^2. For r = 12, V = (4/3) * 3.14 * 1728 = 7234.56 and A = 4 * 3.14 * 144 = 1808.64.
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$4$ mm
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$7$ mm
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$6$ mm
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$5$ mm
B
Correct answer
Explanation
Surface area of a sphere = 4*pi*r^2 = 616. 4 * (22/7) * r^2 = 616. r^2 = 616 * 7 / 88 = 49. r = 7 mm.
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$\displaystyle 30.493{ cm }^{ 3 }$
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$\displaystyle 13.493{ cm }^{ 3 }$
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$\displaystyle 23.493{ cm }^{ 3 }$
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$\displaystyle 33.493{ cm }^{ 3 }$
D
Correct answer
Explanation
Volume of a sphere = (4/3) * pi * r^3. V = (4/3) * 3.14159 * 2^3 = (4/3) * 3.14159 * 8 = 32 * 3.14159 / 3 = 33.5103. Option D is the closest value.
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$2$ in
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$5$ in
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$8$ in
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$7$ in
D
Correct answer
Explanation
Volume = 4/3 * pi * r^3 = 1150.35. r^3 = 1150.35 * 3 / (4 * 3.14) = 3451.05 / 12.56 = 274.76. The cube root of 274.76 is approximately 6.5, which rounds to 7.
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$2$ cm
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$5$ cm
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$6$ cm
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$7 $ cm
C
Correct answer
Explanation
Volume = (4/3) * pi * r^3 = 904.77. r^3 = 904.77 * 3 / (4 * 3.14159) = 216. r = cube root of 216 = 6.
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$12$ cm
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$10$ cm
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$11$ cm
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$9$ cm
B
Correct answer
Explanation
The volume of a hemisphere is (2/3) * pi * r^3. Setting (2/3) * pi * r^3 = 2100 results in r^3 = 2100 * 3 / (2 * 3.14159) which is approximately 1002.67. The cube root of 1002.67 is approximately 10.008, which rounds to 10.
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$\displaystyle 0.1325{ m }^{ 3 }$
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$\displaystyle 0.2325{ cm }^{ 3 }$
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$\displaystyle 0.077{ m }^{ 3 }$
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$\displaystyle 0.325{ mm }^{ 3 }$
C
Correct answer
Explanation
Volume of hemisphere = (2/3) * pi * r^3. With r = 1/3, Volume = (2/3) * 3.14159 * (1/27) = 6.283 / 81 = 0.0775 m^3.
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$\displaystyle 22016{\ m }^{ 2 }$
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$\displaystyle 237.6{\ m }^{ 2 }$
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$\displaystyle 2476{\ m }^{ 2 }$
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None
B
Correct answer
Explanation
Curved surface area of one cylinder = 2 * pi * r * h. r = 0.63 m, h = 15 m. Area = 2 * (22/7) * 0.63 * 15 = 2 * 22 * 0.09 * 15 = 59.4 m^2. For four pillars, area = 4 * 59.4 = 237.6 m^2.