Practice Geometry MCQs for OTS Forest Department Posts Mathematics — topic-wise sets with solved answers.
Q1. What is the radius of a basketball with a volume of approximately 6400 cm³?
Answer: 11.52 cm
Explanation: The correct value is 11.52 cm. Apply the formula or arithmetic step shown in the question and
Q2. A rectangular carpet has an area of 60 sq.m its diagonal and longer side together equal 5 times the shorter side. The length of the carpet is:_________?
Answer: 12m
Explanation: Testing l = 12, w = 5: area = 60 ✓, diagonal = 13, and 13 + 12 = 25 = 5 × 5 ✓; length = 12 m.
Q3. The length of a hall is (4/3) times its breadth. If the area of the hall be 300 square meters the difference between the length and breadth is__________?
Answer: None of these
Explanation: The correct value is None of these. Apply the formula or arithmetic step shown in the question and
Q4. A rectangular field has dimensions 25m by 15m. Two mutually perpendicular passage of 2m width have been left in it's central part and grass has been grown in rest of the field. The area under the grass is____________?
Answer: 299 m²
Explanation: Two perpendicular passages of width 2 m cover: 25×2 + 15×2 − 2×2 = 76 m²; grass area = 375 − 76 = 299 m².
Q5. A 25 cm wide path is to be made around a circular garden having a diameter of 4 meters. Approximate area of the path is square meters is__________?
Answer: 3.34
Explanation: Inner radius = 2 m, outer = 2.25 m; path area = π(2.25² − 2²) = π × 1.0625 ≈ 3.34 m².
Q6. The edge of a cube is 2a cm. Find its surface area?
Answer: 24a^2 cm²
Explanation: Surface area of cube = 6 × side² = 6 × (2a)² = 6 × 4a² = 24a² cm².
Q7. If the perimeter of a sector of a circle with a radius of 6.5 cm is 29 cm, what is its area?
Answer: 52 cm²
Explanation: Arc length = perimeter − 2r = 29 − 13 = 16 cm; area of sector = (1/2) × r × arc = (1/2) × 6.5 × 16 = 52 cm².
Q8. What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
Answer: Rs. 3944
Explanation: The correct value is Rs. 3944. Apply the formula or arithmetic step shown in the question and
Q9. If the length of a rectangle is increased by 20% and it's breadth is decreased by 20% then it area________?
Answer: Decreased by 4%
Explanation: New area = original × 1.20 × 0.80 = 0.96 × original; this is a 4% decrease.
Q10. In a Circle of Radius 5 cm if AB and AC are two equal chords of length 6cm each, then the length of chord BC is___________?
Answer: None of these
Explanation: The correct value is None of these. Apply the formula or arithmetic step shown in the question and
Q11. The difference between the circumference and the radius of a circle is 37 cm. What is the area of the circle?
Answer: 154 cm²
Explanation: 2πr − r = 37 → r(2π − 1) = 37 → r = 7 cm; area = πr² = π × 49 ≈ 154 cm².
Q12. The area of a rectangle is 297 sq cm. If its length is increased by 3 cm and its width is decreased by 1 cm, its area is increased by 3 sq cm. Find the original length and width of the rectangle. Geometric Measurement
Answer: 11 cm and 27 cm
Explanation: The correct value is 11 cm and 27 cm. Apply the formula or arithmetic step shown in the question and
Q13. The area of a circle is 275 cm². What is the circumference of the circle?
Answer: 58.79 cm
Explanation: r = √(275/π) ≈ 9.356 cm; circumference = 2πr ≈ 58.79 cm.
Q14. The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
Answer: 91.5 cm
Explanation: Arc length = (135/360) × 2π × 21 = 49.5 cm; perimeter = 49.5 + 2×21 = 91.5 cm.
Q15. The perimeter of a semi circle is 144 cm then the radius is_________?
Answer: 28 cm
Explanation: Perimeter = πr + 2r = r(π + 2) = 144 → r = 144/5.1416 ≈ 28 cm.
Q16. The perimeter of a circle and a square field are equal. What is the diameter of the circle field if the area of the square field is 484 sq.m?
Answer: 28m
Explanation: The correct value is 28m. Apply the formula or arithmetic step shown in the question and
Q17. How many tiles, each with an area of 10 square inches, are required to cover a floor with dimensions of 5 feet by 4 feet?
Answer: 288
Explanation: Floor area = 5×4 = 20 sq ft = 20 × 144 = 2880 sq inches; tiles needed = 2880/10 = 288.
Q18. What is the area of a triangle having a base of 19m and a height of 7m?
Answer: 66.5 m²
Explanation: Area of triangle = (1/2) × base × height = (1/2) × 19 × 7 = 66.5 m².
Q19. The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?
Answer: 32 m
Explanation: Length = 2w; pond area = 64 m²; field area = 2w² = 8 × 64 = 512 → w = 16, length = 32 m.
Q20. The lengths of the diagonals of a rhombus are 24 cm and 18 cm. What is the length of each side of the rhombus?
Answer: 15 cm
Explanation: Half-diagonals are 12 and 9; side = √(12² + 9²) = √225 = 15 cm.
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