Quantitative Aptitude
Mensuration
2,507 Questions
Mensuration Questions
A
Correct answer
Explanation
The number of balls is the ratio of the volume of the large sphere to the volume of one small ball. (4/3 * pi * 10^3) / (4/3 * pi * 1^3) = 1000 / 1 = 1000.
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2.5 cm
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2.7 cm
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2.1 cm
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2 cm
C
Correct answer
Explanation
Volume of cone = 1/3 * pi * r^2 * h. V1 = 1/3 * pi * 2.1^2 * 4.1. V2 = 1/3 * pi * 2.1^2 * 4.3. Total V = 1/3 * pi * 2.1^2 * (4.1 + 4.3) = 1/3 * pi * 2.1^2 * 8.4. Sphere volume = 4/3 * pi * R^3. 4/3 * pi * R^3 = 1/3 * pi * 2.1^2 * 8.4. 4R^3 = 2.1^2 * 8.4. R^3 = 2.1^2 * 2.1 = 2.1^3. R = 2.1.
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$ \displaystyle 616\sqrt{5}cm^{3} $
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$ \displaystyle 616/\sqrt{5}cm^{3} $
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$ \displaystyle 616\sqrt{3}cm^{3} $
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$ \displaystyle 616\sqrt{2}cm^{3} $
D
Correct answer
Explanation
Volume of new sphere = sum of volumes of three spheres. (4/3) * pi * R^3 = (4/3) * pi * (6^3 + 8^3 + 10^3). R^3 = 216 + 512 + 1000 = 1728. R = cube root of 1728 = 12 cm. Since 12 is not listed, 'none' is correct.
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15400 cm$\displaystyle ^{2}$
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1540 cm$\displaystyle ^{2}$
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154 cm$\displaystyle ^{2}$
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15.400 cm$\displaystyle ^{2}$
A
Correct answer
Explanation
The surface area of a sphere is given by 4 * pi * r^2. Using r = 35 and pi = 22/7, the area is 4 * (22/7) * 35 * 35 = 4 * 22 * 5 * 35 = 15400 cm^2.
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$17600$ $cm^3$
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$16600$ $cm^3$
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$156600$ $m^3$
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None of these
A
Correct answer
Explanation
Rolling a paper of width 14cm along its width means the height of the cylinder is 14cm. The circumference of the base is the length of the paper, but here the radius is given as 20cm. Volume = pi * r^2 * h = 3.14 * 20^2 * 14 = 3.14 * 400 * 14 = 17584, which is approximately 17600.
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$2\pi r^2$
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$2\pi rh^2$
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$2\pi rh$
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None
C
Correct answer
Explanation
The lateral surface area of a cylinder is the circumference of the base multiplied by the height, which is 2 * pi * r * h.
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2 $\times$ area of rectangle $+$ area of circle
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2 $\times$ area of circle $+$ area of rectangle
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2 $\times$ area of square $+$ area of rectangle
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2 $\times$ area of rectangle $+$ area of rectangle
B
Correct answer
Explanation
The total surface area of a cylinder consists of two circular bases (2 * area of circle) and the curved lateral surface, which unfolds into a rectangle (area of rectangle).
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$\displaystyle \pi { r }^{ 2 }$
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$\displaystyle 2\pi rh$
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$\displaystyle 2\pi { r }^{ 2 }$
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$\displaystyle 2\pi r$
B
Correct answer
Explanation
The curved surface area of a cylinder is the circumference of the base multiplied by the height, which is 2 * pi * r * h.
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555 m$^3$
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545 m$^3$
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535 m$^3$
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525 m$^3$
A
Correct answer
Explanation
Volume of truncated cone = (1/3) * pi * h * (r1^2 + r2^2 + r1*r2). Given r1=1.5, r2=2, h=60, pi=3. Volume = (1/3) * 3 * 60 * (1.5^2 + 2^2 + 1.5*2) = 60 * (2.25 + 4 + 3) = 60 * 9.25 = 555.
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781.28 mm$^3$
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791.28 mm$^3$
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761.28 mm$^3$
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711.28 mm$^3$
B
Correct answer
Explanation
Volume of frustum = (1/3) * pi * h * (R^2 + r^2 + R*r). V = (1/3) * 3.14 * 27 * (4^2 + 2^2 + 4*2) = 3.14 * 9 * (16 + 4 + 8) = 3.14 * 9 * 28 = 791.28.
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$\pi r(r+h)$
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$\pi rl(r+h)$
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$2\pi r(r+h)$
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$2\pi r^2l(r+h)$
C
Correct answer
Explanation
The total surface area of a cylinder includes the curved surface area (2 * pi * r * h) plus the areas of the two circular bases (2 * pi * r^2). Summing these gives 2 * pi * r * (h + r).
C
Correct answer
Explanation
Volume = s^3 = 8, so s = 2. Surface area = 6 * s^2 = 6 * 4 = 24.
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$1223\ cm^{3}$
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$1979\ cm^{3}$
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$1323\ cm^{3}$
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$1332\ cm^{3}$
B
Correct answer
Explanation
At 5 paise per cm^2, a cost of Rs 35.20 corresponds to a curved surface area of 704 cm^2. Using pi r l = 704 with l = 25 cm gives r = 8.96 cm. The height is about 23.35 cm, and V = (1/3)pi r^2h is approximately 1979 cm^3.
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$98.56$ cm$^2$
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$68.56$ cm$^2$
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$38.56$ cm$^2$
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None of these
A
Correct answer
Explanation
The surface area of a sphere is given by 4 * pi * r^2. Using r = 2.8 and pi = 22/7, the calculation is 4 * (22/7) * 2.8 * 2.8 = 4 * 22 * 0.4 * 2.8 = 98.56 cm^2.