Quantitative Aptitude
Mensuration
2,507 Questions
Mensuration Questions
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$45m^{2}$
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$54 m^2$
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$50 m^2$
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$48 m^2$
A
Correct answer
Explanation
The square base that fits inside a circular cross-section has diagonal 3 m, so its side is 3/sqrt(2) m. The remaining timber is a square prism with volume 45 cubic m, not 45 square m, so the numerical value matches but the stated unit is wrong.
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$35.2cm^2$
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$38.5cm^2$
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$41.7cm^2$
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$47.6cm^2$
B
Correct answer
Explanation
Circumference = 2 * pi * r = 22. r = 22 / (2 * 22/7) = 3.5 cm. Area = pi * r^2 = (22/7) * 3.5 * 3.5 = 38.5 cm^2.
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$\displaystyle \pi $
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$\displaystyle { \pi }^{ 2 }$
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$\displaystyle { \pi }^{ 3 }$
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$\displaystyle 3\pi $
C
Correct answer
Explanation
Area = pi * r^2. If r = pi, Area = pi * (pi)^2 = pi^3.
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$10m$
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$15cm$
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$20m$
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$24cm$
A
Correct answer
Explanation
The area of the new circle is the sum of the areas of the two given circles: pi*R^2 = pi*(d1/2)^2 + pi*(d2/2)^2. Substituting diameters 16m and 12m gives R^2 = 8^2 + 6^2 = 64 + 36 = 100, so R = 10m.
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$9:4$
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$16:81$
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$4:9$
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$2:3$
B
Correct answer
Explanation
The ratio of the areas of two circles is the square of the ratio of their circumferences. Since the ratio of circumferences is 4:9, the ratio of their areas is 4^2 : 9^2, which is 16:81.
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$\displaystyle \frac{144}{3}cm^{2}$
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$\displaystyle \frac{77}{3}cm^{2}$
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$\displaystyle \frac{154}{7}cm^{2}$
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None
B
Correct answer
Explanation
The area of a sector of a circle is calculated using the formula (theta / 360) * pi * r^2. Substituting the given values of theta = 60 degrees and r = 7 cm, we get (60 / 360) * (22 / 7) * 7^2. This simplifies to (1 / 6) * 154, which reduces to 77 / 3 square centimeters.
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$\displaystyle 22\sqrt{115}m^{2}$
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$\displaystyle 310m^{2}$
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$\displaystyle 22\sqrt{373}m^{2}$
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$\displaystyle 276m^{2}$
C
Correct answer
Explanation
Interpreting the stated volume as 924 m^3, use (1/3)pi r^2 x 18 = 924 to obtain r = 7 m. The slant height is sqrt(7^2 + 18^2) = sqrt(373), so the lateral area is pi x 7 x sqrt(373) = 22sqrt(373) m^2.
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$\displaystyle 24m^{2}$
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$\displaystyle 33m^{2}$
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$\displaystyle 21m^{2}$
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$\displaystyle 27m^{2}$
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$Rs 2000$
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$Rs 2400$
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$Rs 3400$
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$Rs 4400$
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$4 : 9$
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$3 : 2$
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$\displaystyle \sqrt{3}:\sqrt{2}$
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$9 : 4$
D
Correct answer
Explanation
The surface area of a sphere is proportional to the square of its radius (A = 4*pi*r^2). If the ratio of radii is 3:2, the ratio of surface areas is 3^2 : 2^2 = 9:4.
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$96\%$
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$100\%$
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$80\%$
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$126\%$
A
Correct answer
Explanation
Area A = pi * r^2. If r increases by 40%, new radius r' = 1.4r. New area A' = pi * (1.4r)^2 = 1.96 * pi * r^2. The increase is 1.96 - 1 = 0.96, which is 96%.
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44 lit
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88 lit
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66 lit
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None of the above
B
Correct answer
Explanation
Volume = cross-section area * flow rate * time. Area = pi * r^2 = pi * (2 cm)^2 = 4 * pi cm^2. Flow rate = 7 m/min = 700 cm/min. Time = 10 min. Volume = 4 * pi * 700 * 10 = 28,000 * pi cm^3. Since 1000 cm^3 = 1 liter, Volume = 28 * pi liters = 28 * 3.14 = 87.92 liters, which is approx 88 liters.
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$\displaystyle 4\left ( 9-\pi \right )cm^{2}$
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$\displaystyle 9\left ( 4-\pi \right )cm^{2}$
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$\displaystyle 5\left ( 6-\pi \right )cm^{2}$
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$\displaystyle 6\left ( 5-\pi \right )cm^{2}$
B
Correct answer
Explanation
Four circles of radius r=3 form a square of side 2r=6 connecting their centers. The area of the square is 6*6 = 36. The area of the four sectors inside the square is 4 * (90/360 * pi * r^2) = pi * r^2 = 9*pi. The region between them is 36 - 9*pi = 9(4-pi).
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$\displaystyle 20\sqrt{2},20\sqrt{3},10$
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$\displaystyle \frac{10\sqrt{3}}{3},\frac{10\sqrt{2}}{3},\frac{10}{3}$
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$\displaystyle 10\sqrt{3},10\sqrt{2},10$
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$17,14,10$
C
Correct answer
Explanation
The total area is pi*R^2 = pi*20^2 = 400*pi. Dividing into 4 equal parts means each ring/circle has area 100*pi. The radii r1, r2, r3 satisfy pi*r3^2 = 100*pi (r3=10), pi*r2^2 = 200*pi (r2=10*sqrt(2)), and pi*r1^2 = 300*pi (r1=10*sqrt(3)).