Quantitative Aptitude
Mensuration
2,507 Questions
Mensuration Questions
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$440sq.cm$
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$880sq.cm$
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$88sq.cm$
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$44sq.cm$
B
Correct answer
Explanation
Lateral surface area of a cylinder = circumference * height = 44 * 20 = 880 sq.cm.
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$36.98\pi \ \text{cm}^{2}$, $59.26\pi \ \text{cm}^{2}$
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$48.1\pi \ \text{cm}^{2}$, $58.22\pi \ \text{cm}^{2}$
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$36.98\pi \ \text{cm}^{2}$, $59.88\pi \ \text{cm}^{2}$
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$49.1\pi \ \text{cm}^{2}$, $5.32\pi \ \text{cm}^{2}$
C
Correct answer
Explanation
Curved surface area of hollow hemisphere = 2 * pi * (R^2 + r^2) = 2 * pi * (4.3^2 + 2.1^2) = 2 * pi * (18.49 + 4.41) = 45.8 pi. Total surface area = CSA + pi * (R^2 - r^2) = 45.8 pi + pi * (18.49 - 4.41) = 59.88 pi. The provided option C matches the TSA.
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$616\ {cm}^{3}$
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$66 \ {cm}^{3}$
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$16 \ {cm}^{3}$
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None of these
A
Correct answer
Explanation
Circumference = 2 * pi * r = 44, so r = 7 m. Height h = 12 m. Volume = (1/3) * pi * r^2 * h = (1/3) * (22/7) * 49 * 12 = 22 * 7 * 4 = 616 m^3. Note: The unit in the option is cm^3, which is a typo for m^3.
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$1200{cm}^{3}$
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$360{cm}^{3}$
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$40{cm}^{3}$
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$90{cm}^{3}$
C
Correct answer
Explanation
Volume of cylinder = pi * r^2 * h = 120. Volume of cone = 1/3 * pi * r^2 * h. Since r and h are the same, volume of cone = 1/3 * 120 = 40.
C
Correct answer
Explanation
The volume of a cylinder is given by V = pi * r^2 * h. Substituting the given values, 550 = (22/7) * 5^2 * h. Solving for h, we get h = (550 * 7) / (22 * 25) = 3850 / 550 = 7.
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$\cfrac { 27\pi }{ 24 } $
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$\cfrac { 5\pi }{ 24 } $
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$\cfrac { 3\pi }{ 4 } $
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None of these
B
Correct answer
Explanation
Volume of a spherical cap is (pi * h^2 / 3) * (3R - h). Here R=1, h=1/2. V = (pi * (1/4) / 3) * (3 - 1/2) = (pi / 12) * (5/2) = 5 * pi / 24.
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Rs. $90$
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Rs. $97$
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Rs. $110$
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Rs. $95$
C
Correct answer
Explanation
Curved surface area = 2 * pi * r * h = 2 * (22/7) * 2.5 * 14 = 220 m^2. Cost = 220 * 0.50 = 110.
D
Correct answer
Explanation
Volume of large sphere = (4/3) * pi * 8^3. Volume of small sphere = (4/3) * pi * 1^3. Number of spheres = 8^3 / 1^3 = 512.
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$\pi 2r (l + r) $
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$\pi r \left (l + \dfrac{r}{4}\right)$
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$\pi r (l + r) $
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$2\pi rl$
B
Correct answer
Explanation
Total surface area of a cone = pi * radius * (slant height + radius). Given radius = r/2 and slant height = 2l. Area = pi * (r/2) * (2l + r/2) = pi * r * (l + r/4).
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$188.57$
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$190.8$
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$185.3$
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$181.56$
A
Correct answer
Explanation
Revolving a 6-8-10 triangle about the 8cm side creates a cone with height h=8 and radius r=6. Slant height l = 10. Curved surface area = pi * r * l = 3.14159 * 6 * 10 = 188.49. Closest option is 188.57.
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$241.74\ m^2$
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$240\ m^2$
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$250.48\ m^2$
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$260\ m^2$
A
Correct answer
Explanation
For the tent, 165 = π(5)l gives a slant height of about 10.5 m. The vertical height is about 9.23 m, so the volume is (1/3)π(5^2)(9.23) ≈ 241.74 m^3.
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Rs. $47.50$
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Rs. $56.12$
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Rs. $68.75$
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Rs. $75.12$
C
Correct answer
Explanation
Diameter = 0.5 m, r = 0.25 m, h = 3.5 m. Curved surface area = 2 * pi * r * h = 2 * (22/7) * 0.25 * 3.5 = 5.5 m^2. Cost = 5.5 * 12.50 = 68.75.
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$4 \pi r h + 4 \pi r^2$
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$4 \pi r h $
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$ \pi r h + \pi r^2$
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$4 \pi r h - \pi r^2$
A
Correct answer
Explanation
Two cylinders stacked: height becomes 2h. Total surface area = 2 * pi * r^2 (top and bottom) + 2 * pi * r * (2h) (side area). This equals 2 * pi * r^2 + 4 * pi * r * h.
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$462\ { cm }^{ 2 }$
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$344.35\ { cm }^{ 2 }$
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$498.35\ { cm }^{ 2 }$
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$None\ of\ these$
C
Correct answer
Explanation
Total surface area of a cone = pi * r * (r + l), where l = sqrt(r^2 + h^2). r = 7, h = 14, l = sqrt(49 + 196) = sqrt(245) approx 15.65. Area = 3.14 * 7 * (7 + 15.65) = 21.98 * 22.65 approx 497.8. Option C is the closest.
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$21$ cm
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$23$ cm
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$25$ cm
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$19$ cm
A
Correct answer
Explanation
The volume of the cuboid is 49 * 33 * 24 = 38808 cm^3. The volume of a sphere is (4/3) * pi * r^3. Setting (4/3) * (22/7) * r^3 = 38808, we get r^3 = 38808 * 21 / 88 = 9261. The cube root of 9261 is 21.