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Indian Coast Guard Yantrik Mensuration — practice questions

Explore 60 free Mensuration questions in Indian Coast Guard Yantrik Quantitative Aptitude. Open each question or exercise to read its content, reference answers and available explanation.

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Mensuration questions and exercises with answers

Showing questions 1–30 of 60.

In a right triangle, if one leg is 9 cm and hypotenuse is 15 cm, the other leg isRead the answer and worked solution →In an equilateral triangle of side 6 cm, the area isRead the answer and worked solution →The angles of a triangle are in the ratio 2 : 3 : 4. The largest angle isRead the answer and worked solution →Two similar triangles have their sides in the ratio 3 : 5. The ratio of their areas isRead the answer and worked solution →In triangle ABC, AB = AC and angle A = 40 degrees. Then angle B isRead the answer and worked solution →The circumference of a circle with diameter 14 cm is (use pi = 22/7)Read the answer and worked solution →If two chords AB and CD of a circle intersect at P inside the circle, with PA = 4, PB = 9, PC = 6, then PD isRead the answer and worked solution →The radius of a circle whose area is 154 cm^2 is (use pi = 22/7)Read the answer and worked solution →The angle subtended by a diameter at any point on the circle isRead the answer and worked solution →Sum of all interior angles of a regular hexagon isRead the answer and worked solution →Each interior angle of a regular octagon isRead the answer and worked solution →The number of sides of a regular polygon whose each exterior angle is 30 degrees isRead the answer and worked solution →The volume of a cube of side 5 cm isRead the answer and worked solution →The total surface area of a cube of side 6 cm isRead the answer and worked solution →The volume of a sphere of radius 7 cm is (use pi = 22/7)Read the answer and worked solution →The slant height of a cone with radius 6 cm and height 8 cm isRead the answer and worked solution →The lateral (curved) surface area of a cone with radius 5 cm and slant height 13 cm isRead the answer and worked solution →The value of cos 0 degrees + sin 90 degrees isRead the answer and worked solution →The value of sin^2(30) + cos^2(30) isRead the answer and worked solution →If sin(theta) = 3/5, then cos(theta) is (theta acute)Read the answer and worked solution →The value of sin(60) x cos(30) isRead the answer and worked solution →If tan(theta) = sqrt(3), then theta isRead the answer and worked solution →If sec(theta) = 5/4, then tan(theta) isRead the answer and worked solution →From a point 30 m away from the foot of a tower, the angle of elevation of the top is 45 degrees. The height of the tower isRead the answer and worked solution →A pole is broken at a height. The broken part touches ground 10 m from the foot at an angle of 30 degrees with the ground. The original total height of the pole isRead the answer and worked solution →If sin(theta) + cos(theta) = sqrt(2), then sin(theta) isRead the answer and worked solution →The distance between points (3, 4) and (0, 0) isRead the answer and worked solution →If sin(theta) + cos(theta) = sqrt(2) and theta is acute, then theta isRead the answer and worked solution →The midpoint of segment joining (2, 3) and (6, 7) isRead the answer and worked solution →The line 2x + 3y = 12 has y-interceptRead the answer and worked solution →

Worked practice questions

In a right triangle, if one leg is 9 cm and hypotenuse is 15 cm, the other leg is

  1. 11 cm
  2. 12 cm
  3. 13 cm
  4. 10 cm
Show answer and solution

Correct answer: B. 12 cm

**Pythagoras:** sqrt(15^2 - 9^2) = sqrt(225 - 81) = sqrt(144) = 12 cm. Classic 9-12-15 triple (3x of 3-4-5).

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In an equilateral triangle of side 6 cm, the area is

  1. 6 sqrt(3) cm^2
  2. 9 sqrt(3) cm^2
  3. 12 sqrt(3) cm^2
  4. 18 sqrt(3) cm^2
Show answer and solution

Correct answer: B. 9 sqrt(3) cm^2

Area = (sqrt(3)/4) x s^2 = (sqrt(3)/4) x 36 = 9 sqrt(3) cm^2.

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The angles of a triangle are in the ratio 2 : 3 : 4. The largest angle is

  1. 80 degrees
  2. 90 degrees
  3. 60 degrees
  4. 70 degrees
Show answer and solution

Correct answer: A. 80 degrees

Sum of parts = 9; each part = 180/9 = 20 degrees. Largest = 4 x 20 = 80 degrees.

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