Quantitative Aptitude
Mensuration
2,507 Questions
Mensuration Questions
D
Correct answer
Explanation
Area = pi * r^2 = (22/7) * 7 * 7 = 22 * 7 = 154 m^2.
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154 cm2
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308 cm2
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616 cm2
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1078 cm2
C
Correct answer
Explanation
Circumference = 2 * pi * r = 88. So, r = 88 / (2 * pi) = 44 / (22/7) = 14 cm. Area = pi * r^2 = (22/7) * 14 * 14 = 22 * 2 * 14 = 616 cm^2.
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324.7 cm3
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311.5 cm3
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281.4 cm3
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269.5 cm3
D
Correct answer
Explanation
Lateral surface area (LSA) = 2*pi*r*h = 154. Total surface area (TSA) = 2*pi*r*h + 2*pi*r^2. Given LSA/TSA = 2/3, we have 154 / (154 + 2*pi*r^2) = 2/3. Solving this gives 2*pi*r^2 = 77. Using LSA=154, we find r=3.5 and h=7. Volume = pi*r^2*h = 269.5.
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156.4 sq.in
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188.4 sq.in
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264.3 sq.in
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423.9 sq.in
B
Correct answer
Explanation
Volume = 1/3 * pi * r^2 * h = 301.44. With r=3k and h=4k, 1/3 * 3.14 * 9k^2 * 4k = 301.44 => 37.68k^3 = 301.44 => k^3 = 8 => k=2. So r=6, h=8. Slant height l = sqrt(6^2 + 8^2) = 10. Lateral surface area = pi * r * l = 3.14 * 6 * 10 = 188.4.
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352 sq. cm
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380 sq. cm
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448 sq. cm
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496 sq. cm
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540 sq. cm
C
Correct answer
Explanation
Volume 1 = 2.5*4*8 = 80. Volume 2 = 4*9*12 = 432. Total volume = 512. New solid: 16*4*h = 512 => 64h = 512 => h = 8. Surface area = 2(lw + lh + wh) = 2(16*4 + 16*8 + 4*8) = 2(64 + 128 + 32) = 2(224) = 448.
C
Correct answer
Explanation
The diameter is the distance between (4, -2) and (6, -14). Diameter^2 = (6-4)^2 + (-14 - (-2))^2 = 2^2 + (-12)^2 = 4 + 144 = 148. Radius^2 = Diameter^2 / 4 = 148 / 4 = 37. Area = pi * r^2 = 37 pi.
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1102 cu. cm
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1078 cu. cm
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981 cu. cm
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841 cu. cm
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655 cu. cm
B
Correct answer
Explanation
LSA = 2*pi*r*h, TSA = 2*pi*r*h + 2*pi*r^2. Ratio LSA/TSA = 1/2 implies 2*pi*r*h = 2*pi*r^2, so h = r. TSA = 2*pi*r*h + 2*pi*r^2 = 4*pi*r^2 = 616. r^2 = 616 / (4 * 22/7) = 49, so r = 7. Volume = pi*r^2*h = pi*7^2*7 = 22/7 * 49 * 7 = 1078.
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4712 cm2
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4730.8 cm2
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4739.2 cm2
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3297 cm2
D
Correct answer
Explanation
Curved surface area of a cylinder = 2 * pi * r * h. Area = 2 * (22/7) * 15 * 35 = 2 * 22 * 15 * 5 = 3300. The provided options seem to use a different pi or are incorrect. Recalculating with pi = 3.14159: 2 * 3.14159 * 15 * 35 = 3298.6. Option D is the closest.
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3,632 cu. in
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3,642 cu. in
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3,768 cu. in
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3,832 cu. in
C
Correct answer
Explanation
CSA = 2 * pi * r * h = 753.6. Given r/h = 5/6, let r = 5x and h = 6x. 2 * 3.14 * 5x * 6x = 753.6 => 188.4 * x^2 = 753.6 => x^2 = 4 => x = 2. So r = 10, h = 12. Volume = pi * r^2 * h = 3.14 * 100 * 12 = 3768.
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375.4 sq. inches
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398.5 sq. inches
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405.24 sq. inches
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452.16 sq. inches
D
Correct answer
Explanation
Radius = 12. Area = pi * r^2 = 3.14 * 144 = 452.16.
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18.2 seconds
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19.2 seconds
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21.2 seconds
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23.2 seconds
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268 sq. cm
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458 sq. cm
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462 sq. cm
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528 sq. cm
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624 sq. cm
D
Correct answer
Explanation
The curved surface area of a cone is given by the formula pi * r * l, where r is the radius and l is the slant height. Using pi = 22/7, the area is (22/7) * 6 * 28 = 22 * 6 * 4 = 528 sq. cm.
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164 cm2
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254 cm2
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168 cm2
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154 cm2
D
Correct answer
Explanation
The curved surface area of a frustum is pi * (r1 + r2) * l. Using pi = 22/7, r1 = 4, r2 = 3, and l = 7, we get (22/7) * (4 + 3) * 7 = 22 * 7 = 154 cm^2.
A
Correct answer
Explanation
Volume of original cylinder = pi * 7^2 * 15 = 735 * pi. Two new cylinders have volume = 2 * (pi * r^2 * 7.5) = 15 * pi * r^2. 735 * pi = 15 * pi * r^2. r^2 = 735 / 15 = 49. r = 7.
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220 cm2
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200 cm2
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320 cm2
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300 cm2
A
Correct answer
Explanation
Curved surface area of a frustum = pi * l * (r1 + r2). CSA = (22/7) * 14 * (3 + 2) = 22 * 2 * 5 = 220 cm^2.