Quantitative Aptitude
Mensuration
2,507 Questions
Mensuration Questions
A
Correct answer
Explanation
Volume V = pi * r^2 * h. If r and h increase by 20%, the new volume V' = pi * (1.2r)^2 * (1.2h) = pi * 1.44r^2 * 1.2h = 1.728 * V. The increase is 72.8%.
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$\displaystyle \left ( 440+25\pi \right )cm^{2} $
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$\displaystyle \left ( 440+50\pi \right )cm^{2} $
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$\displaystyle 440 cm^{2} $
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None of these
C
Correct answer
Explanation
Volume V = pi * r^2 * h = 1100. r = 5. pi * 25 * h = 1100 => h = 1100 / (25 * pi) = 44 / pi. Curved surface area = 2 * pi * r * h = 2 * pi * 5 * (44 / pi) = 10 * 44 = 440.
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$\displaystyle 3\sqrt{34}m $
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$\displaystyle 2\sqrt{28}m $
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$\displaystyle 2\sqrt{44}m $
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$\displaystyle 2\sqrt{34}m $
D
Correct answer
Explanation
Ratio r:h = 3:5, so r = 3x, h = 5x. Volume = (1/3) * pi * r^2 * h = 120 * pi. (1/3) * pi * (9x^2) * (5x) = 120 * pi. 15x^3 = 120, so x^3 = 8, x = 2. Thus r = 6, h = 10. Slant height l = sqrt(r^2 + h^2) = sqrt(36 + 100) = sqrt(136) = 2 * sqrt(34).
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$\displaystyle\frac{2}{3}\pi r^2h$
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$\pi r^2h$
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$2\pi r^3h$
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$\displaystyle\frac{1}{3}\pi r^2h$
A
Correct answer
Explanation
The volume of a cone is (1/3) * pi * r^2 * height. Substituting the given height 2h, the volume is (1/3) * pi * r^2 * (2h) = (2/3) * pi * r^2 * h.
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$\displaystyle 12\pi $
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$\displaystyle 36\pi $
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$\displaystyle 72\pi $
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$\displaystyle 144\pi $
D
Correct answer
Explanation
Volume of a cone = (1/3) * pi * r^2 * h. Volume = (1/3) * pi * 6^2 * 12 = (1/3) * pi * 36 * 12 = 144 * pi.
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$10$ cm
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$15$ cm
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$20$ cm
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$40$ cm
C
Correct answer
Explanation
Curved surface area = 2 * pi * r * h = 1760. 2 * (22/7) * 14 * h = 1760. 88 * h = 1760. h = 20.
A
Correct answer
Explanation
The cylinder's curved surface area is 2πrh, and the cone's is πrl. Thus, 2h:l = 8:5, so l = 5h/4. Using l^2 = r^2 + h^2 gives r:h = 3:4.
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$2.1$ cm
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$2$ cm
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$4.2$ cm
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$3.1$ cm
A
Correct answer
Explanation
Volume of sphere = sum of volumes of two cones. (4/3)piR^3 = (1/3)pir^2h1 + (1/3)pir^2h2. (4/3)R^3 = (1/3)r^2(h1+h2). 4R^3 = (2.1)^2 * (4.1+4.3) = 4.41 * 8.4 = 37.044. R^3 = 37.044 / 4 = 9.261. R = cube root of 9.261 = 2.1.
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$\displaystyle 450cm^{2}$
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$\displaystyle 500cm^{2}$
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$\displaystyle 550cm^{2}$
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$\displaystyle 600cm^{2}$
C
Correct answer
Explanation
Volume V = (1/3) * pi * r^2 * h = 1232. (1/3) * (22/7) * r^2 * 24 = 1232. 8 * (22/7) * r^2 = 1232. r^2 = 1232 * 7 / 176 = 49. So r = 7. Slant height l = sqrt(r^2 + h^2) = sqrt(49 + 576) = sqrt(625) = 25. Curved surface area = pi * r * l = (22/7) * 7 * 25 = 550.
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$8\pi r^2 cm^2$
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$4\pi r^2 cm^2$
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$5\pi r^2 cm^2$
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$6\pi r^2 cm^2$
D
Correct answer
Explanation
A solid sphere has a surface area of 4*pi*r^2. When bisected, two hemispheres are created. Each hemisphere has a curved surface area of 2*pi*r^2 and a flat circular base of pi*r^2, totaling 3*pi*r^2 per piece. For two pieces, the total surface area is 6*pi*r^2.
D
Correct answer
Explanation
Volume = (4/3) * pi * r^3. Surface Area = 4 * pi * r^2. Equating them: (4/3) * pi * r^3 = 4 * pi * r^2. Dividing by 4 * pi * r^2 gives r/3 = 1, so r = 3.
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$1000 cm^3$
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$1200 cm^3$
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$1100 cm^3$
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$900 cm^3$
A
Correct answer
Explanation
The surface area of a cube is 6a^2 = 600, so a^2 = 100, which means a = 10 cm. The volume is a^3 = 10^3 = 1000 cm^3.
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$77$
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$154$
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$38 . 5$
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$308$
B
Correct answer
Explanation
The side of the square is 44 cm. When joined to form a cylinder, the circumference of the base is 44 cm. 2 * pi * r = 44. r = 44 / (2 * 22/7) = 7. Base area = pi * r^2 = 22/7 * 7 * 7 = 154.
B
Correct answer
Explanation
Volume of cylinder = pi * r^2 * h = pi * 25 * 10 = 250pi. Volume of cone = 1/3 * pi * r^2 * h = 1/3 * pi * 25 * 10 = 250pi / 3. Number of cones = (250pi) / (250pi / 3) = 3.
B
Correct answer
Explanation
Original volume V = pi * r^2 * h. New volume 1: pi * (r+y)^2 * h = V. New volume 2: pi * r^2 * (h+4y) = V. Given r=6, h=6, we have (6+y)^2 * 6 = 6^2 * (6+4y). Solving (6+y)^2 = 6(6+4y) leads to 36 + 12y + y^2 = 36 + 24y, so y^2 = 12y, y = 12.