Quantitative Aptitude
Mensuration
2,507 Questions
Mensuration Questions
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$20$%
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$40$%
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$72.2$%
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$72.8$%
D
Correct answer
Explanation
Volume V = (1/3) * pi * r^2 * h. New volume V' = (1/3) * pi * (1.2r)^2 * (1.2h) = (1/3) * pi * 1.44r^2 * 1.2h = 1.728 * V. Increase = 72.8%.
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$\displaystyle h\, =\, \frac{1}{3}\, r$
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$\displaystyle h\, =\, \frac{1}{2}\, r$
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$h = r$
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$h = 2r$
B
Correct answer
Explanation
Curved surface area (CSA) = 2*pi*r*h. Total surface area (TSA) = 2*pi*r*h + 2*pi*r^2. Given CSA = 1/3 * TSA. 2*pi*r*h = 1/3 * (2*pi*r*h + 2*pi*r^2). 6*pi*r*h = 2*pi*r*h + 2*pi*r^2. 4*pi*r*h = 2*pi*r^2. 2h = r, so h = r/2.
C
Correct answer
Explanation
Volume of large sphere = (4/3) * pi * 8^3. Volume of small sphere = (4/3) * pi * 1^3. Number of balls n = (8^3) / (1^3) = 512.
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$110{m}^{2}$
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$210{m}^{2}$
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$140{m}^{2}$
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$250{m}^{2}$
A
Correct answer
Explanation
Inner curved surface area = 2 * pi * r * h. Diameter = 3.5 m, so r = 1.75 m. CSA = 2 * (22/7) * 1.75 * 10 = 2 * 22 * 0.25 * 10 = 110 m^2.
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$394.24{cm}^{2}$
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$394.42\ cm^2$
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$493.24\ cm^2$
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$493.42\ cm^2$
A
Correct answer
Explanation
Surface area of a sphere = 4 * pi * r^2. Using pi = 3.14, 4 * 3.14 * (5.6)^2 = 12.56 * 31.36 = 393.88. Using pi = 22/7, 4 * (22/7) * 5.6 * 5.6 = 88 * 0.8 * 5.6 = 394.24.
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$2\times \cfrac{22}{7}\times \cfrac{21}{10}\times \cfrac{45}{10}{m}^{2}$
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$2\times \cfrac{12}{7}\times \cfrac{21}{10}\times \cfrac{45}{10}{m}^{2}$
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$2\times \cfrac{22}{7}\times \cfrac{11}{10}\times \cfrac{45}{10}{m}^{2}$
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$2\times \cfrac{22}{7}\times \cfrac{21}{10}\times \cfrac{35}{10}{m}^{2}$
A
Correct answer
Explanation
Curved surface area = 2 * pi * r * h. Diameter = 4.2, so radius r = 2.1 = 21/10. Height h = 4.5 = 45/10. Area = 2 * (22/7) * (21/10) * (45/10). This matches option A.
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Rs.$4400$
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Rs.$3400$
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Rs.$2400$
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Rs.$4300$
A
Correct answer
Explanation
The curved surface area of a cylinder is 2 * pi * r * h. With diameter 3.5m, radius is 1.75m. Area = 2 * (22/7) * 1.75 * 10 = 110 m^2. Cost = 110 * 40 = 4400.
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$1386\ {cm}^{2}$
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$1836\ cm^2$
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$1368\ cm^2$
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$1683\ cm^2$
A
Correct answer
Explanation
Surface area of a sphere = 4 * pi * r^2. Using pi = 22/7, SA = 4 * (22/7) * (10.5)^2 = 4 * (22/7) * 110.25 = 88 * 15.75 = 1386.
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$3.5$ cm
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$4.5$ cm
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$4$ cm
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$3$ cm
A
Correct answer
Explanation
Surface area of sphere = 4*pi*r^2 = 154. 4 * (22/7) * r^2 = 154. r^2 = (154 * 7) / (4 * 22) = 7 * 7 / 4 = 49/4. r = 7/2 = 3.5.
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$173\ {cm}^{2}$
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$133\ {cm}^{2}$
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$143\ {cm}^{2}$
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$273\ {cm}^{2}$
A
Correct answer
Explanation
Inner radius = 5 cm, thickness = 0.25 cm, so outer radius R = 5.25 cm. The outer curved surface area of a hemisphere is 2 * pi * R^2. 2 * 3.14 * (5.25)^2 = 2 * 3.14 * 27.5625 = 173.29, which rounds to 173.
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$6.4$ cm
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$6$ cm
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$4$ cm
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$4.8$ cm
A
Correct answer
Explanation
Volume of cone = (1/3) * pi * r^2 * h. Since volume is constant, r1^2 * h1 = r2^2 * h2. (1.6)^2 * 3.6 = (1.2)^2 * h2. 2.56 * 3.6 = 1.44 * h2. h2 = (2.56 * 3.6) / 1.44 = 6.4 cm.
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$\displaystyle \frac {2\pi p^{3}}{15}$
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$\displaystyle \frac {4\pi p^{3}}{15}$
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$\displaystyle \frac {\pi p^{3}}{15}$
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$\displaystyle \frac {\pi p^{3}}{12}$
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$1.75\ m$
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$2.75\ m$
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$1.25\ m$
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$3.75\ m$
A
Correct answer
Explanation
Curved surface area = Total cost / rate = 2200 / 20 = 110 m^2. Formula for CSA = 2 * pi * r * h. 110 = 2 * (22/7) * r * 10. 110 = (440/7) * r. r = 110 * 7 / 440 = 7/4 = 1.75 m.
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$141.3\ {cm}^{3}$
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$241.3\ {cm}^{3}$
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$131.3\ {cm}^{3}$
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$121.3\ {cm}^{3}$
A
Correct answer
Explanation
Lateral surface area = 2 * pi * r * h = 94.3. 2 * 3.14 * r * 5 = 94.3. 31.4 * r = 94.3. r = 3. Volume = pi * r^2 * h = 3.14 * 9 * 5 = 141.3.