Quantitative Aptitude
Mensuration
2,507 Questions
Mensuration Questions
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$2210$ $\displaystyle cm^{3}$
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$2310$ $\displaystyle cm^{3}$
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$2010$ $\displaystyle cm^{3}$
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$2110$ $\displaystyle cm^{3}$
B
Correct answer
Explanation
The volume of a cylinder is pi * r^2 * h. Using pi = 22/7, r = 7, and h = 15: (22/7) * 49 * 15 = 22 * 7 * 15 = 154 * 15 = 2310.
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10500 $\displaystyle cm^{3}$
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10450 $\displaystyle cm^{3}$
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10000 $\displaystyle cm^{3}$
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None of the above
B
Correct answer
Explanation
Volume of frustum = (1/3) * pi * h * (R^2 + r^2 + R*r). R=15, r=10, h=21. V = (1/3) * (22/7) * 21 * (225 + 100 + 150) = 22 * 475 = 10450.
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$14$ cm
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$411$ cm
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$\displaystyle \sqrt{2464}$ cm
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$1232$ cm
A
Correct answer
Explanation
The surface area of a sphere is given by 4 * pi * r^2. Setting 4 * pi * r^2 = 2464 and using pi = 22/7, we get 4 * (22/7) * r^2 = 2464, which simplifies to r^2 = 196. Thus, r = 14 cm.
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$\displaystyle 385000cm^{2}$
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$\displaystyle 358000cm^{2}$
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$\displaystyle 835000cm^{2}$
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$\displaystyle 345000cm^{2}$
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792 $ \displaystyle cm^{3} $
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892 $ \displaystyle cm^{3} $
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992 $ \displaystyle cm^{3} $
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none of these
A
Correct answer
Explanation
Volume of cylinder = pi * r^2 * h = pi * 6^2 * 11 = 396 * pi. Volume of hemisphere = (2/3) * pi * r^3 = (2/3) * pi * 6^3 = 144 * pi. Remaining volume = 396 * pi - 144 * pi = 252 * pi. Using pi approx 3.14, 252 * 3.14 = 791.28, which rounds to 792.
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0.5 cm
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1.0 cm
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1.25 cm
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1.5 cm
C
Correct answer
Explanation
Volume of solid = 22 * 7 * 5 = 770 cm^3. Volume of cylinder rise = pi * r^2 * h. 770 = (22/7) * 14 * 14 * h. 770 = 22 * 2 * 14 * h = 616 * h. h = 770 / 616 = 1.25 cm.
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$ \displaystyle 22 cm^{3} $
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$ \displaystyle 44 cm^{3} $
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$ \displaystyle 88 cm^{3} $
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$ \displaystyle 99 cm^{3} $
C
Correct answer
Explanation
Volume of a cylinder = pi * r^2 * h. Using pi = 22/7, V = (22/7) * 2^2 * 7 = 22 * 4 = 88 cm^3.
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330 cm$\displaystyle ^{3}$
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660 cm$\displaystyle ^{2}$
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990 cm$\displaystyle ^{2}$
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1320 cm$\displaystyle ^{2}$
B
Correct answer
Explanation
Total surface area of a hollow cylinder = 2 * pi * (R + r) * h + 2 * pi * (R^2 - r^2). R = 3+1 = 4, r = 3, h = 14. Area = 2 * pi * (4+3) * 14 + 2 * pi * (16 - 9) = 2 * pi * 7 * 14 + 2 * pi * 7 = 196 * pi + 14 * pi = 210 * pi. Using pi = 22/7, Area = 210 * 22/7 = 30 * 22 = 660.
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1078 $cm^3$
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1708 $cm^3$
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1780 $cm^3$
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1068 $cm^3$
A
Correct answer
Explanation
Volume of a cylinder = pi * r^2 * h = 22/7 * 7 * 7 * 7 = 22 * 49 = 1078.
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15 cm
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20 cm
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10 cm
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None of these
B
Correct answer
Explanation
The volume of a cylinder is pi * r^2 * h. Given V = 3080 and r = 7, 3080 = (22/7) * 7^2 * h. 3080 = 22 * 7 * h = 154 * h. h = 3080 / 154 = 20 cm.
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$\displaystyle 169.56{ ft }^{ 3 }$
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$\displaystyle 169.46{ ft }^{ 3 }$
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$\displaystyle 168.46{ ft }^{ 3 }$
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$\displaystyle 159.20{ ft }^{ 3 }$
A
Correct answer
Explanation
Volume of a cylinder = pi * r^2 * h. Volume = 3.14 * (3)^2 * 6 = 3.14 * 9 * 6 = 3.14 * 54 = 169.56.
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200,000 ft$^3$
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220,000 ft$^3$
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210,000 ft$^3$
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230,000 ft$^3$
C
Correct answer
Explanation
The volume of a frustum is (1/3) * pi * h * (R^2 + r^2 + R*r). Given R=20, r=10, h=300, and pi=3: Volume = (1/3) * 3 * 300 * (20^2 + 10^2 + 20*10) = 300 * (400 + 100 + 200) = 300 * 700 = 210,000 ft^3.
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181,300 in$^3$
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171,300 in$^3$
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161,300 in$^3$
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151,300 in$^3$
B
Correct answer
Explanation
Volume of frustum = (1/3) * pi * h * (R^2 + r^2 + R*r). With R=21, r=5, h=300, and pi=3: V = (1/3) * 3 * 300 * (21^2 + 5^2 + 21*5) = 300 * (441 + 25 + 105) = 300 * 571 = 171,300 in^3.
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30.76 mm
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11.25 mm
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12.25 mm
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13.25 mm
A
Correct answer
Explanation
The volume of a frustum is V = (h/3) * (A1 + A2 + sqrt(A1 * A2)). Given V = 1600, A1 = 16, and A2 = 100, we have 1600 = (h/3) * (16 + 100 + sqrt(1600)). This simplifies to 1600 = (h/3) * (116 + 40) = (h/3) * 156. Thus, 1600 = 52h, so h = 1600/52 = 30.769 mm.