Quantitative Aptitude
Mensuration
2,507 Questions
Mensuration Questions
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$112\ m$
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$110\ m$
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$114\ m$
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$116\ m$
A
Correct answer
Explanation
Volume of cuboid = 4.4 * 2.6 * 1 = 11.44 m^3. Hollow pipe volume = pi * (R^2 - r^2) * L. Internal radius r = 0.3 m, thickness = 0.05 m, so external radius R = 0.35 m. Volume = pi * (0.35^2 - 0.3^2) * L = pi * (0.1225 - 0.09) * L = pi * 0.0325 * L. 11.44 = (22/7) * 0.0325 * L. Solving for L gives 112 m.
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$6 cm$
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$8 cm$
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$12 cm$
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$10 cm$
A
Correct answer
Explanation
Surface area of a sphere is 4 * pi * r^2. Given 4 * pi * r^2 = 144 * pi, we have r^2 = 36, so r = 6 cm.
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$12\pi r^2$
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$8\pi r^2$
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$6\pi r^2$
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$3\pi r^2$
A
Correct answer
Explanation
The total surface area of a solid hemisphere is given by the formula 3 * pi * R^2. Substituting R = 2r into the formula gives 3 * pi * (2r)^2 = 3 * pi * 4r^2 = 12 * pi * r^2.
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$3.5 cm$
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$7cm$
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$10.5cm$
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$11cm$
A
Correct answer
Explanation
The curved surface area of a hemisphere is 2 * pi * r^2. Given 2 * pi * r^2 = 77, r^2 = 77 / (2 * 3.14159) = 12.25. r = sqrt(12.25) = 3.5 cm.
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1000 $m^{3}$
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100 $m^{3}$
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25 $m^{3}$
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125 $m^{3}$
D
Correct answer
Explanation
Lateral surface area of a cube = 4 * a^2 = 100. So a^2 = 25, a = 5. Volume = a^3 = 5^3 = 125 m^3.
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$3\ cm$
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$6\ cm$
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$11\ cm$
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$24\ cm$
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$12cm$
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$8cm$
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$10cm$
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$18cm$
A
Correct answer
Explanation
In a right-angled triangle formed by the height, radius, and slant height of a cone, h^2 + r^2 = l^2. h^2 + 5^2 = 13^2 => h^2 + 25 = 169 => h^2 = 144 => h = 12.
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$288 \pi cm^{3}$
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$108 \pi cm^{3}$
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$144 \pi cm^{3}$
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$72 \pi cm^{3}$
C
Correct answer
Explanation
Area of base of hemisphere = pi * r^2 = 36 * pi. r^2 = 36, r = 6. Volume of hemisphere = (2/3) * pi * r^3 = (2/3) * pi * 216 = 144 * pi.
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$4 \pi a^2 cm$
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$2 \pi a^2 cm^2$
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$3 \pi a^2 cm$
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$8 \pi a^2 cm^2$
A
Correct answer
Explanation
A cylinder that just encloses a sphere of radius a has cylinder radius a and height 2a. Its curved surface area is 2pi x a x 2a = 4pi a^2.
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$18 \sqrt{5} \, cm^2.$
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$5 \sqrt{18}\pi \, cm^2.$
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$18 \sqrt{5}\pi \, cm^2.$
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$5 \sqrt{18} \, cm^2.$
C
Correct answer
Explanation
Let legs be x and 9-x. Volume V = (1/3) * pi * r^2 * h. If rotated about leg h, r = 9-h. V = (1/3) * pi * (9-h)^2 * h. dV/dh = (pi/3) * ((9-h)^2 - 2h(9-h)) = 0. (9-h)(9-h-2h) = 0. h = 3, r = 6. Lateral area = pi * r * l = pi * r * sqrt(r^2 + h^2) = pi * 6 * sqrt(36 + 9) = pi * 6 * sqrt(45) = pi * 6 * 3 * sqrt(5) = 18 * sqrt(5) * pi.
A
Correct answer
Explanation
Let radius of sphere = r. Height of cylinder = 2r. Curved surface area of cylinder = 2 * pi * r * h = 2 * pi * r * (2r) = 4 * pi * r^2. Surface area of sphere = 4 * pi * r^2. The ratio is 1:1.
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$200\%$
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$500\%$
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$700\%$
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$800\%$
C
Correct answer
Explanation
Volume of a sphere is proportional to r^3. If radius increases by 100%, the new radius is 2r. The new volume is proportional to (2r)^3 = 8r^3. The increase is (8r^3 - r^3) / r^3 = 7, which is 700%.
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No real value of $x$
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One integer value of $x$
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One rational, but not integral, value of $x$
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One irrational value of $x$
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Two real values of $x$
D
Correct answer
Explanation
The volume of the cylinder is pi * R^2 * H = pi * 3^2 * 5 = 45 * pi cubic centimeters. Since 1 mm equals 0.1 cm, the volume of each cone is (1/3) * pi * r^2 * h = (1/3) * pi * 0.1^2 * 1 = pi / 300 cubic centimeters. Dividing the cylinder's volume by the cone's volume gives 45 * pi / (pi / 300) = 13,500 cones.
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$1 : 2 : 3$
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$1 : 4 : 6$
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$1 : 6 : 9$
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$1 : 7 : 19$
D
Correct answer
Explanation
The cone portions are determined by cumulative heights from the vertex. At one-third and two-thirds of the altitude, the similar cones have volumes 1/27 and 8/27 of the whole cone. The three separated volumes are therefore 1/27, 7/27, and 19/27, giving the ratio 1:7:19.