Quantitative Aptitude
Mensuration
2,507 Questions
Mensuration Questions
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$5x^{2}$
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$6x^{2}$
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$\dfrac {200}{x} + x^{2}$
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$\dfrac {200}{x} + 2x^{2}$
C
Correct answer
Explanation
Volume V = x^2 * h = 50, so h = 50/x^2. The surface area of an open-top box with a square base is the base area (x^2) plus four side faces (4 * x * h). Substituting h, we get x^2 + 4 * x * (50/x^2) = x^2 + 200/x.
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$x$
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$\dfrac{x}{^3\sqrt{2}}$
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$^3\sqrt{2}$
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$\dfrac{1}{^3\sqrt{2}}$
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$^3\sqrt{2x}$
B
Correct answer
Explanation
The cone volume is (1/3)pi x^2(2x) = (2/3)pi x^3. Equating this to the sphere volume (4/3)pi r^3 gives r^3 = x^3/2. Hence, r = x/cuberoot(2).
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$5.00$
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$5.50$
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$6.24$
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$8.06$
D
Correct answer
Explanation
The volume of a sphere is (4/3) * pi * r^3. With r=5, volume = (4/3) * pi * 125 = 523.6. A cube with volume s^3 = 523.6 has an edge length s = cbrt(523.6) which is approximately 8.06.
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$\pi r\left [ \sqrt{r^{2}+h^{2}}+3r+2h \right ]$
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$\pi r\left [ \sqrt{r^{2}+h^{2}}+2r+3h \right ]$
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$\pi r\left [2 \sqrt{r^{2}+h^{2}}+3r+2h \right ]$
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none of these
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$15cm$
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$18cm$
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$20cm$
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$25cm$
C
Correct answer
Explanation
Lateral surface area of a cube = 4 * side^2. 4 * a^2 = 1600, so a^2 = 400, a = 20 cm.
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$284cm^2$
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$286cm^2$
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$296cm^2$
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$300cm^2$
B
Correct answer
Explanation
The volume of the metal sheet is 27 * 8 * 1 = 216 cm^3. A cube with this volume has a side length of 6 cm. The surface area of the sheet is 2 * (27*8 + 8*1 + 27*1) = 2 * (216 + 8 + 27) = 502 cm^2. The surface area of the cube is 6 * 6^2 = 216 cm^2. The difference is 502 - 216 = 286 cm^2.
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$15$
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$15\sqrt 3$
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$3\sqrt 6$
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$5\sqrt 3$
A
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. Equating: 88 * r^2 = 19800. r^2 = 19800 / 88 = 225. r = 15.
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$2.35$ cm.
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$2.30$ cm.
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$2.25$ cm.
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$2.15$ cm.
C
Correct answer
Explanation
Volume of sphere = (4/3) * pi * 3^3 = 36 * pi. This volume displaces water in the cylinder: pi * r^2 * h = 36 * pi. With r = 4, pi * 16 * h = 36 * pi, so h = 36 / 16 = 2.25 cm.
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$\dfrac { 2500 }{ 3 } \pi { cm }^{ 3 }$
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$5000\pi { cm }^{ 3 }\quad $
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$2500\pi { cm }^{ 3 }\quad $
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$\dfrac { 5000 }{ 3 } \pi { cm }^{ 3 }$
A
Correct answer
Explanation
Cylinder radius 5, height 100 (10 balls of radius 5). Volume cylinder = pi * 5^2 * 100 = 2500pi. Volume 10 spheres = 10 * (4/3) * pi * 5^3 = 10 * (4/3) * 125 * pi = 5000pi/3. Empty space = 2500pi - 5000pi/3 = 2500pi/3.
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$660 cm^2$
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$770 cm^2$
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$880 cm^2$
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$990 cm^2$
B
Correct answer
Explanation
Surface area = CSA of cylinder + CSA of hemisphere + CSA of cone. CSA_cyl = 2*pi*r*h = 2*pi*5*13 = 130*pi. CSA_hemi = 2*pi*r^2 = 2*pi*25 = 50*pi. CSA_cone = pi*r*l. Slant height l = sqrt(r^2 + h^2) = sqrt(5^2 + 12^2) = 13. CSA_cone = pi*5*13 = 65*pi. Total = (130+50+65)*pi = 245*pi. 245 * 3.14 = 769.3, which rounds to 770.
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$5120$
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$8960$
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$4830$
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$6400$
A
Correct answer
Explanation
Original sheet 48x36. Cut 8m squares from corners. New dimensions: 48-16=32, 36-16=20. Height=8. Volume = 32 * 20 * 8 = 5120.
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$8.5$ cm
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$10.5$ cm
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$19.5$ cm
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none
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$V=\frac {\pi r^2}{3}(h+H+2r)$
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$V=\frac {\pi r^2}{3}(h+2H+2r)$
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$V=\frac {\pi r^2}{3}(h+3H+4r)$
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$V=\frac {\pi r^2}{3}(h+3H+2r)$
D
Correct answer
Explanation
Total volume = Volume of cylinder + Volume of cone + Volume of hemisphere. V = pi*r^2*H + (1/3)*pi*r^2*h + (2/3)*pi*r^3. Factoring out (pi*r^2)/3 gives (pi*r^2)/3 * (3H + h + 2r).
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1428 $cm^2$
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1524 $cm^2$
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1380 $cm^2$
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1200 $cm^2$
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Rs. 12,947
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Rs. 13,947
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Rs. 14,947
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Rs. 15,947
B
Correct answer
Explanation
The cone's height is 16 - 6 = 10 m. Its slant height is sqrt(10^2 + 2^2) = sqrt(104) m, so the canvas area is 2π(2)(6) + π(2)sqrt(104), approximately 139.47 m^2. At Rs. 100 per m^2, the cost is approximately Rs. 13,947.