Level 1
Geometry MCQs set 3 for High Court Clerk / Reader (Lahore / Peshawar) Mathematics — 20 solved questions.
Q1. If the volume of a sphere and a cone are equal and they have the same radius (r), what is the height (h) of the cone in terms of r?
Answer: h=4r
Explanation: The correct value is h=4r. Apply the formula or arithmetic step shown in the question and
Q2. What is the perimeter of a square field whose diagonal is 8√2?
Answer: 32 m
Explanation: For a square with diagonal d, side = d/√2 = 8√2/√2 = 8 m. Perimeter = 4 × 8 = 32 m.
Q3. If an area enclosed by a circle or a square or an equal triangle is the same then the maximum perimeter is possessed by_________?
Answer: Equilateral Triangle
Explanation: For a fixed area, the shape with the greatest perimeter is the equilateral triangle, as its perimeter grows faster than that of a square or circle.
Q4. In a triangle ABC, if angle C = 90°, angle A = 30°, and the hypotenuse AB is 10 cm, what is the length of side BC?
Answer: 5 cm
Explanation: In a 30-60-90 triangle, the side opposite 30° is half the hypotenuse: BC = 10 × sin 30° = 5 cm.
Q5. The altitude of an equilateral triangle of side 2√3 cm is_________?
Answer: 3 cm
Explanation: Altitude of equilateral triangle = (√3/2) × side = (√3/2) × 2√3 = 3 cm.
Q6. The area of a rhombus in 2016 Sq.cm and its side is 65cm. The length of its diagonals are________?
Answer: 126cm,32cm
Explanation: Half-diagonals a and b satisfy a²+b²=65²=4225 and (1/2)×2a×2b=2016, so ab=2016. Solving: diagonals are 126 cm and 32 cm (63²+16²=3969+256=4225 ✓).
Q7. If a right circular cone-shaped building has a radius of 8m and a slant height of 17m, what is its volume?
Answer: 320 πm³
Explanation: Height = √(17² − 8²) = √225 = 15 m; volume = (1/3)πr²h = (1/3) × π × 64 × 15 = 320π m³.
Q8. The radius of a wire is decreased to one -third if volume remains the same length will increase:
Answer: 9 times
Explanation: Volume = πr²l is constant. With new radius r/3: π(r/3)²l' = πr²l, so l' = 9l. The length increases 9 times.
Q9. If the radius of circle is increased by 20% its area is increased by:
Answer: 44%
Explanation: New area = π(1.2r)² = 1.44πr²; the area increases by 44%. Show the calculation clearly when solving similar quantitative items.
Q10. Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm. Geometric Measurement
Answer: 285 cm2
Explanation: Area of trapezium = ½ × (sum of parallel sides) × height = ½ × (20 + 18) × 15 = 285 cm².
Q11. The areas of two similar triangles are 12 cm^2 and 48SQ. cm. If the height of the smaller one is 2.1cm, then the corresponding height of the bigger one is _________? (Note: the symbol ^ indicates power)
Answer: 4.2cm
Explanation: The ratio of corresponding heights equals the square root of the ratio of areas: √(48/12) = 2; larger height = 2 × 2.1 = 4.2 cm.
Q12. The edges of a cuboid are 4 cm, 5 cm and 6 cm. Find the volume of the cuboid?
Answer: 120 cm³
Explanation: Volume of a cuboid = length × width × height = 4 × 5 × 6 = 120 cm³.
Q13. The area of a parallelogram is 128sq m and its altitude is twice the corresponding base. Then the length of the base is_________?
Answer: 8 m
Explanation: Area = base × height = b × 2b = 2b² = 128, so b² = 64 and base = 8 m.
Q14. The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is_________?
Answer: 80 m
Explanation: Area of trapezium = ½ × (sum of parallel sides) × depth. 640 = ½ × (10+6) × d → d = 640/8 = 80 m.
Q15. If the volume of a cylinder is 360 cm³, what is the volume of a cone with the same height and base?
Answer: 120 cm³
Explanation: A cone with the same base and height as a cylinder holds exactly 1/3 of the cylinder's volume: 360 ÷ 3 = 120 cm³.
Q16. Find the area of a parallelogram with base 24 cm and height 16 cm. Geometric Measurement
Answer: 384 cm2
Explanation: Area of a parallelogram = base × height = 24 × 16 = 384 cm².
Q17. The radius of a circle is increased by 1%. Find how much % does its area increases?
Answer: 2.01%
Explanation: New area = π(1.01r)² = 1.0201πr²; the area increases by 2.01%. Show the calculation clearly when solving similar quantitative items.
Q18. What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?
Answer: 498.35 cm²
Explanation: The correct value is 498.35 cm². Apply the formula or arithmetic step shown in the question and
Q19. The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
Answer: 2
Explanation: With perimeter 28 the sides sum to 14; setting up (a²+b²)/ab = 25/12 and using a+b = 14 gives a−b = 2.
Q20. What is the height of a parallelogram with an area of 54 cm² and a base of 15 cm?
Answer: 3.6 cm
Explanation: Height of parallelogram = Area ÷ base = 54 ÷ 15 = 3.6 cm.