Quantitative Aptitude
Mensuration
2,507 Questions
Mensuration Questions
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$1$ cm
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$2$ cm
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$4$ cm
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$6$ cm
D
Correct answer
Explanation
The volume of the cone is (1/3) * pi * r^2 * h = (1/3) * pi * 6^2 * 24 = 288 * pi. The volume of the sphere is (4/3) * pi * R^3. Setting them equal: (4/3) * pi * R^3 = 288 * pi, which gives R^3 = 216, so R = 6.
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$\displaystyle \dfrac{3}{5}$
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$\displaystyle \dfrac{5}{6}$
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$\displaystyle \dfrac{4}{5}$
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$\displaystyle \dfrac{8}{9}$
B
Correct answer
Explanation
Curved surface area = 2*pi*r*h. Ratio = (2*pi*r1*h1) / (2*pi*r2*h2) = (r1/r2) * (h1/h2) = (2/3) * (5/4) = 10/12 = 5/6.
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$900$ $\displaystyle cm^{2}$
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$960$ $\displaystyle cm^{2}$
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$968$ $\displaystyle cm^{2}$
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$964$ $\displaystyle cm^{2}$
C
Correct answer
Explanation
Inner curved surface area = 2 * pi * r * h. Diameter = 4, so r = 2. h = 77. Area = 2 * (22/7) * 2 * 77 = 2 * 22 * 2 * 11 = 968.
D
Correct answer
Explanation
Curved surface area = 2 * pi * r * h = 4.4. 2 * (22/7) * 0.7 * h = 4.4. 4.4 * h = 4.4, so h = 1.
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$523.9 \ \displaystyle cm^{3}$
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$520.91 \ \displaystyle cm^{3}$
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$512.91 \ \displaystyle cm^{3}$
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$510.91 \ \displaystyle cm^{3}$
A
Correct answer
Explanation
The volume of a hemisphere is (2/3) * pi * r^3. Using r = 6.3 and pi = 22/7: (2/3) * (22/7) * (6.3)^3 = (2/3) * (22/7) * 250.047 = 523.9056. Rounding to one decimal place gives 523.9.
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20 cu cm
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22 cu cm
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28 cu cm
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24 cu cm
D
Correct answer
Explanation
The volume of a cuboid is calculated as length * width * height. Here, 4 * 3 * 2 = 24.
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$125.6\:m$
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$1256\:m$
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$12.56\:m$
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$1.256\:m$
A
Correct answer
Explanation
Length of cylinder = 1.2m = 120cm. Diameter = 10cm. Circumference = pi * 10 = 31.4cm. Number of turns = 120cm / 0.3cm = 400 turns. Total length = 400 * 31.4cm = 12560cm = 125.6m.
C
Correct answer
Explanation
The curved surface area of a cylinder is 2*pi*r*h = 264, and the volume is pi*r^2*h = 924. Dividing the volume by the surface area gives (pi*r^2*h) / (2*pi*r*h) = 924 / 264, which simplifies to r/2 = 3.5, so r = 7. The diameter is 2*r = 14 m.
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$2 : 3$
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$1 : 1$
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$2 : 1$
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$1 : 2$
C
Correct answer
Explanation
Curved surface area = 2*pi*r*h. Area of ends = 2 * (pi*r^2). Given 2*pi*r*h = 2 * (2*pi*r^2), which simplifies to h = 2r. Thus, h/r = 2/1.
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$\displaystyle 2\pi r^{2}$
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$\displaystyle 3\pi r^{2}$
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$\displaystyle 4\pi r^{2}$
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$\displaystyle 8\pi r^{2}$
A
Correct answer
Explanation
The curved surface area of a sphere is 4 * pi * r^2. A hemisphere is half of a sphere, so its curved surface area is 2 * pi * r^2.
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$9\pi\:cm^3$
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$15\pi\:cm^3$
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$21\pi\:cm^3$
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$24\pi\:cm^3$
D
Correct answer
Explanation
Volume of cylinder = pi * r^2 * h = pi * 3^2 * 4 = 36 * pi. Volume of cone = 1/3 * pi * r^2 * h = 1/3 * pi * 3^2 * 4 = 12 * pi. Remaining volume = 36 * pi - 12 * pi = 24 * pi.
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$2\ units$
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$3\ units$
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$5\ units$
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$8\ units$
B
Correct answer
Explanation
(4/3)pi r^3 = 4pi r^2. Dividing by 4pi r^2 gives r/3 = 1, so r = 3.
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$\displaystyle 603cm^{3}$
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$\displaystyle 720cm^{3}$
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$\displaystyle 548cm^{3}$
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$\displaystyle 637cm^{3}$
A
Correct answer
Explanation
Volume of cylinder = pi * r^2 * h = pi * 6^2 * 8 = 288 * pi. Volume of cone = 1/3 * pi * r^2 * h = 1/3 * pi * 6^2 * 8 = 96 * pi. Remaining volume = 288 * pi - 96 * pi = 192 * pi. Using pi approx 3.14159, 192 * 3.14159 = 603.18, which rounds to 603.
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$\displaystyle 88m^{2}$
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$\displaystyle 78m^{2}$
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$\displaystyle 80m^{2}$
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$\displaystyle 70m^{2}$
A
Correct answer
Explanation
Area covered in one revolution = circumference * length = (2 * pi * r) * h. Area = 2 * (22/7) * 0.7 * 2 = 8.8 m^2. In 10 revolutions, area = 88 m^2.
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$\displaystyle \frac{352}{21}m^{3}$
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$\displaystyle 576m^{3}$
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$\displaystyle \frac{376}{9}m^{3}$
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$\displaystyle 600m^{3}$
A
Correct answer
Explanation
The volume of a hemisphere is (2/3)πr^3. For r = 2 cm, this is (2/3)π(8) = 16π/3 cm^3, approximately 352/21 cm^3 using π = 22/7. The numerical answer matches option A, but its displayed unit should be cm^3, not m^3.