Quantitative Aptitude
Mensuration
2,507 Questions
Mensuration Questions
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$15\pi$
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$225\pi$
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$400\pi$
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$900\pi$
B
Correct answer
Explanation
Circumference C = 2 * pi * r = 30 * pi, so r = 15. The area A = pi * r^2 = pi * 15^2 = 225 * pi.
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$700$%
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$500$%
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$300$%
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$100$%
A
Correct answer
Explanation
New radius R = 2r, new height H = 2h. New volume = (1/3) * pi * (2r)^2 * (2h) = 8 * (1/3) * pi * r^2 * h = 8 * original volume. Increase = 8V - V = 7V, which is 700%.
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$48 cm^2$
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$64 cm^2$
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$80 cm^2$
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none of these
C
Correct answer
Explanation
The figure formed by joining midpoints of a rhombus is a rectangle. Its area is half the area of the rhombus. Area of rhombus = (d1 * d2) / 2 = (16 * 20) / 2 = 160. Area of rectangle = 160 / 2 = 80.
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$Rs. 13,440$
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$Rs. 3340$
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$Rs. 14,200$
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$Rs. 13,520.$
A
Correct answer
Explanation
Area = s^2 = 7056, so s = sqrt(7056) = 84 m. Perimeter = 4 * 84 = 336 m. Five layers of wiring = 5 * 336 = 1680 m. Total cost = 1680 * 8 = 13440.
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$75$ sq. cm
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$50$ sq. cm
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$225$ sq. cm
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$15$ sq. cm
C
Correct answer
Explanation
The perimeter of a square is 4 * side. Given 4 * side = 60, the side length is 15 cm. The area is side squared, which is 15 * 15 = 225 sq. cm.
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$6.4cm$
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$5.4cm$
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$1.4cm$
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$3.4cm$
B
Correct answer
Explanation
Volume of tube = pi * (R^2 - r^2) * h = pi * (3.5^2 - 3^2) * 21 = pi * (12.25 - 9) * 21 = pi * 3.25 * 21 = 68.25 * pi. Volume of cone = (1/3) * pi * r^2 * h = (1/3) * pi * r^2 * 7. Setting them equal: 68.25 = (7/3) * r^2. r^2 = 68.25 * 3 / 7 = 29.25. r = sqrt(29.25) approx 5.4.
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$\dfrac {10}{8}cm$
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$\dfrac {18}{5}cm$
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$\dfrac {10}{9}cm$
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$\dfrac {1}{9}cm$
B
Correct answer
Explanation
The volume of the sphere is (4/3) * pi * r^3 = (4/3) * pi * (7.5)^3. The water level drop is equal to the volume of the sphere divided by the cross-sectional area of the jar (pi * 12.5^2). Calculation: (4/3 * pi * 7.5^3) / (pi * 12.5^2) = (4/3 * 421.875) / 156.25 = 562.5 / 156.25 = 3.6 cm, which is 18/5 cm.
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$204.3\ \text{ cm }^{ 2 }$(approx)
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$102.8\ \text{ cm }^{ 2 }$(approx)
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$40.8\ \text{ cm }^{ 2 }$(approx)
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$52\ \text{ cm }^{ 2 }$(approx)
A
Correct answer
Explanation
Curved surface area of a cone is pi * r * l, where l = sqrt(r^2 + h^2). With r=5 and h=12, l = sqrt(25 + 144) = 13. Area = 3.14 * 5 * 13 = 204.1. Option A is the closest.
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$94.29\, cm^3$
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$108.25\, cm^3$
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$48.52\, cm^3$
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$90.28\, cm^3$
A
Correct answer
Explanation
Volume = Volume of hemisphere + Volume of cone. V = (2/3)pi*r^3 + (1/3)*pi*r^2*h. r=3, h=4. V = (1/3)*pi*r^2(2r + h) = (1/3)3.14*9(6+4) = 3*3.14*10 = 94.2 cm^3. The option 94.29 is the closest.
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$\dfrac {3}{14}$
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$\dfrac {5}{13}$
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$\dfrac {14}{23}$
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$\dfrac {7}{3}$
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$1024\ cm^{2}$
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$6032\ cm^{2}$
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$2484\ cm^{2}$
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$2464\ cm^{2}$
D
Correct answer
Explanation
Surface area of a sphere = 4 * pi * r^2. Using pi = 22/7 and r = 14: 4 * (22/7) * 14 * 14 = 4 * 22 * 2 * 14 = 88 * 28 = 2464.
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$12cm$
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$10cm$
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$15 cm$
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$18 cm$
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$660\mathrm { cm } ^ { 2 }$
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$930\mathrm { cm } ^ { 2 }$
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$1320\mathrm { cm } ^ { 2 }$
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$640\mathrm { cm } ^ { 2 }$
A
Correct answer
Explanation
Curved surface area of a cylinder = 2 * pi * r * h. Diameter = 21, so radius r = 10.5. Area = 2 * (22/7) * 10.5 * 10 = 2 * 22 * 1.5 * 10 = 660.
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$1436.03 \ cm^3$
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$87.92 \ cm^3$
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$1345.01 \ cm^3$
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$100.02 \ cm^3$
A
Correct answer
Explanation
The volume of a sphere is (4/3) * pi * r^3. With r = 7 and pi = 3.14, V = (4/3) * 3.14 * 343 = 1436.0266... which rounds to 1436.03.
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$110.6 \ cm^2$
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$128.6 \ cm^2$
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$131.5 \ cm^2$
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None of these
B
Correct answer
Explanation
Surface area of a sphere = 4 * pi * r^2. With r = 3.2, Area = 4 * 3.14159 * (3.2)^2 = 4 * 3.14159 * 10.24 = 128.679. This matches option B.