Quantitative Aptitude
Mensuration
2,507 Questions
Mensuration Questions
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$30\%$
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$40\%$
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$42\%$
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$33.1\%$
D
Correct answer
Explanation
Volume V = pi * r^2 * h. If r and h increase by 10%, the new volume is pi * (1.1r)^2 * (1.1h) = pi * 1.21r^2 * 1.1h = 1.331 * V. This represents a 33.1% increase.
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$10$ cm
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$20$ cm
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$30$ cm
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$40$ cm
D
Correct answer
Explanation
Curved surface area of frustum = pi * (R+r) * l. R=6, r=3. 360 * pi = pi * (6+3) * l = 9 * pi * l. l = 360/9 = 40 cm.
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$43.98$ sq. cm
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$53.67$ sq. cm
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$47.24$ sq. cm
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$38.54$ sq. cm
A
Correct answer
Explanation
Area = pi * (R^2 - r^2) = 3.1416 * (5.7^2 - 4.3^2) = 3.1416 * (32.49 - 18.49) = 3.1416 * 14 = 43.9824.
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$4:1$
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$2:1$
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$3:1$
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None of these
A
Correct answer
Explanation
Let radii be r1 and r2. We have r1 + r2 = 15 and pi(r1^2 + r2^2) = 153pi. Solving r1^2 + r2^2 = 153 and (r1 + r2)^2 = 225, we find 2*r1*r2 = 225 - 153 = 72, so r1*r2 = 36. The roots of x^2 - 15x + 36 = 0 are 12 and 3. The ratio is 12:3 = 4:1.
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$78 cm^2$
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$87 cm^2$
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$88 cm^2$
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$74 cm^2$
C
Correct answer
Explanation
The curved surface area of a cone is given by pi*r*l. Using pi = 22/7, r = 4, and l = 7, the area is (22/7) * 4 * 7 = 88 cm^2.
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$89\ cm^3$
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$589\ cm^3$
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$700\ cm^3$
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$58\ cm^3$
B
Correct answer
Explanation
Volume of sphere = 4/3 * pi * r^3. r = 5.2. Volume = 4/3 * 3.14159 * (5.2)^3 = 4/3 * 3.14159 * 140.608 = 588.98. This rounds to 589.
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$20$ cm, $16$ cm, $8$ cm
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$14$ cm, $12$ cm, $8$ cm
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$11$ cm, $19$ cm, $8$ cm
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$21$ cm, $11$ cm, $8$ cm
A
Correct answer
Explanation
Let dimensions be 5x, 4x, 2x. Surface Area = 2(lw + lh + wh) = 2(20x^2 + 10x^2 + 8x^2) = 2(38x^2) = 76x^2. 76x^2 = 1216 => x^2 = 16 => x = 4. Dimensions are 20, 16, 8.
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$12\pi$
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$15\pi$
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$18\pi$
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$36\pi$
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$\displaystyle\frac{1}{4}\pi r^3$
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$\displaystyle\frac{1}{32}\pi r^3$
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$\pi r^3$
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$\displaystyle\frac{1}{8}\pi r^3$
C
Correct answer
Explanation
The volume of a cylinder is V = pi * r^2 * h. Given r = h, the formula becomes V = pi * r^2 * r = pi * r^3.
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$1386cm^2$
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$1625cm^2$
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$1716cm^2$
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$3087cm^2$
A
Correct answer
Explanation
Volume = (4/3) * pi * r^3 = 4851. r^3 = (4851 * 3) / (4 * 22/7) = 1157.625. r = 10.5. Surface Area = 4 * pi * r^2 = 4 * (22/7) * 10.5 * 10.5 = 1386 cm^2.
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$\sqrt{2}:\sqrt{3}$
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$2:3$
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$4:9$
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$16:81$
C
Correct answer
Explanation
The volume of a hemisphere is proportional to the cube of the radius (V proportional to r^3). The ratio of volumes is 6.4 : 21.6 = 64 : 216 = 8 : 27. Thus, the ratio of radii is the cube root of 8 : 27, which is 2 : 3. The surface area is proportional to the square of the radius (r^2), so the ratio of areas is 2^2 : 3^2 = 4 : 9.
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$8$cm
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$9$cm
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$10$cm
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$12$cm
C
Correct answer
Explanation
Let radius r = 3k and height h = 4k. Volume = (1/3) * pi * r^2 * h = (1/3) * pi * (9k^2) * (4k) = 12 * pi * k^3. Given 12 * pi * k^3 = 96 * pi, so k^3 = 8 and k = 2. Thus, r = 6 and h = 8. The slant height l = sqrt(r^2 + h^2) = sqrt(36 + 64) = 10 cm.
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$4950\ {cm}^{2}$
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$4951\ {cm}^{2}$
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$4952\ {cm}^{2}$
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$4953\ {cm}^{2}$
A
Correct answer
Explanation
Curved surface area of a frustum = pi * (R + r) * l. R = 28, r = 7, l = 45. CSA = (22/7) * (28 + 7) * 45 = (22/7) * 35 * 45 = 22 * 5 * 45 = 110 * 45 = 4950 cm^2.
C
Correct answer
Explanation
Area = pi * 4^2 + pi * 3^2 = 16pi + 9pi = 25pi. New circle area = pi * R^2 = 25pi, so R = 5. Diameter = 2R = 10.
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$\displaystyle \frac { h }{ \sqrt { \pi } } $
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$\displaystyle h\sqrt { \pi } $
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$\displaystyle \frac { \sqrt { \pi } }{ h } $
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$\displaystyle \frac { { h }^{ 2 } }{ \pi } $
A
Correct answer
Explanation
Let the cube edge be s. Volume of cube = s^3. Volume of cylinder = pi * r^2 * h. Given h = s, so volume of cube = h^3. Equating the volumes: pi * r^2 * h = h^3. Dividing by pi * h gives r^2 = h^2 / pi, so r = h / sqrt(pi).