Quantitative Aptitude
Mensuration
2,507 Questions
Mensuration Questions
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$1.05{m}^{3}$
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$3.05{m}^{3}$
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$1.15{m}^{3}$
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$2.05{m}^{3}$
A
Correct answer
Explanation
Volume of a sphere = 4/3 * pi * r^3. V = 4/3 * 3.14 * (0.63)^3 = 4/3 * 3.14 * 0.250047 = 1.047... which is 1.05.
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$5:12$
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$12:5$
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$13:12$
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$5:11$
A
Correct answer
Explanation
When a right triangle is revolved about a leg, it forms a cone where the other leg is the radius and the revolved leg is the height. For the first case (revolved about 12cm), radius r1=5, height h1=12, volume V1 = (1/3) * pi * 5^2 * 12 = 100pi. For the second case (revolved about 5cm), radius r2=12, height h2=5, volume V2 = (1/3) * pi * 12^2 * 5 = 240pi. The ratio V1:V2 is 100:240, which simplifies to 5:12.
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$3.773$ litres
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$3.553$ litres
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$3.223$ litres
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$4.773$ litres
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$5544$
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$1386$
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$8316$
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$4158$
A
Correct answer
Explanation
(4/3) * pi * r^3 = 38808. r^3 = 38808 * 3 / (4 * 3.14159) = 9261. r = 21. Surface area = 4 * pi * r^2 = 4 * (22/7) * 21 * 21 = 5544.
D
Correct answer
Explanation
Curved surface area of a cone = pi * r * l = 188.4. l = sqrt(r^2 + h^2). 3.14 * r * sqrt(r^2 + 8^2) = 188.4. r * sqrt(r^2 + 64) = 60. Square both sides: r^2(r^2 + 64) = 3600. Let u = r^2: u^2 + 64u - 3600 = 0. (u + 100)(u - 36) = 0. u = 36, so r = 6.
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$830 {cm}^{3}$
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$380{cm}^{3}$
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$308{cm}^{3}$
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$803{cm}^{3}$
C
Correct answer
Explanation
Lateral surface area = 2 * pi * r * h = 176. Base area = pi * r^2 = 38.5. From base area, r^2 = 38.5 / (22/7) = 12.25, so r = 3.5. Then 2 * (22/7) * 3.5 * h = 176, so 22 * h = 176, h = 8. Volume = pi * r^2 * h = 38.5 * 8 = 308.
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$20cm$
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$15cm$
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$10cm$
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None
B
Correct answer
Explanation
Volume of cuboid = 44 * 30 * 15 = 19800. Volume of cylinder = pi * r^2 * h = (22/7) * r^2 * 28 = 88 * r^2. Setting 88 * r^2 = 19800 gives r^2 = 225, so r = 15.
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$1100\ {cm}^{2}$
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$2100\ {cm}^{2}$
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$1150\ {cm}^{2}$
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$1200\ {cm}^{2}$
A
Correct answer
Explanation
Total surface area of a cone = pi * r * (r + l). r = 10, l = 25. TSA = (22/7) * 10 * (10 + 25) = (22/7) * 10 * 35 = 22 * 10 * 5 = 1100.
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$4cm$
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$8\pi cm$
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$8cm$
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$16cm$
C
Correct answer
Explanation
The volume of the hollow sphere is (4/3) * pi * r^3. With r=4, volume = (4/3) * pi * 64 = 256pi/3. Half of this is 128pi/3. The volume of the cone is (1/3) * pi * R^2 * h. Setting (1/3) * pi * R^2 * 2 = 128pi/3 leads to 2 * R^2 = 128, so R^2 = 64 and R = 8.
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$6\ cm$
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$8\ cm$
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$4\ cm$
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$5\ cm$
A
Correct answer
Explanation
The volume of a cylinder is given by V = pi * r^2 * h. Substituting the given values, 600 * pi = pi * (10^2) * h, which simplifies to 600 = 100 * h, so h = 6 cm.
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$19.404$ litres
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$16.141$ litres
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$22.254$ litres
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$18.204$ litres
A
Correct answer
Explanation
Volume of a hemisphere = (2/3) * pi * r^3. With r = 21 and pi = 22/7, V = (2/3) * (22/7) * 21^3 = (2/3) * (22/7) * 9261 = 2 * 22 * 441 = 19404 cm^3. Since 1000 cm^3 = 1 litre, this is 19.404 litres.
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$5720\ {cm}^{3}$
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$322000\ {cm}^{3}$
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$472000\ {cm}^{3}$
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$502000\ {cm}^{3}$
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$94$ paise
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Rs. $1.40$
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Rs. $9.40$
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Rs. $19.40$
C
Correct answer
Explanation
Volume = l*b*h = 3x*4x*5x = 60x^3 = 60. So x^3 = 1, x = 1. Dimensions are 3, 4, 5 dm (0.3, 0.4, 0.5 m). Surface area = 2*(0.12 + 0.20 + 0.15) = 2*(0.47) = 0.94 sq m. Cost = 0.94 * 10 = 9.40 rupees.
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$225 cm^{2}$
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$234 cm^{2}$
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$270 cm^{2}$
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$279 cm^{2}$
B
Correct answer
Explanation
A cube has 6 faces. If we glue cubes to 5 faces, we lose 5 faces of the original cube and 5 faces of the new cubes. Original surface area = 6 * 3^2 = 54. 5 new cubes added, each adds 5 exposed faces. Total surface = 54 + 5 * (5 * 3^2) - 5 * 3^2 (covered area) = 54 + 225 - 45 = 234.