Area problems
- 1. A solid hemisphere has radius 14 cm. It is melted to form a cylinder such that the ratio of its curved surface area and total surface area is 2 : 3. What is the radius (in cm) of its base?
Options- A. 1033
- B. 1433
- C. 733
- D. 2133 Discuss
Correct Answer: 1433
- 2. In triangle XYZ, G is the centroid. If XY = 11 cm, YZ = 14 cm and XZ = 7 cm, then what is the value (in cm) of GM?
Options- A. 6
- B. 4
- C. 2
- D. 3 Discuss
Correct Answer: 2
- 3. In the given figure, PQRS is a square inscribed in a circle of radius 4 cm. PQ is produced till point Y. From Y a tangent is drawn to the circle at point R. What is the length (in cm) of SY ?
Options- A. 4√10
- B. 2√10
- C. 6√10
- D. 3√5 Discuss
Correct Answer: 4√10
- 4. In a trapezium, one diagonal divides the other in the ratio 2 : 9. If the length of the larger of the two parallel sides is 45 cm, then what is the length (in cm) of the other parallel side?
Options- A. 10
- B. 5
- C. 18
- D. 14 Discuss
Correct Answer: 10
- 5. The distance between the centres of two circles is 61 cm and their radii are 35 cm and 24 cm. What is the length (in cm) of the direct common tangent to the circles?
Options- A. 60
- B. 54
- C. 48
- D. 72 Discuss
Correct Answer: 60
- 6. In the given figure, PQRS is a quadrilateral. If QR = 18 cmand PS = 9 cm,then what is the area (in sq. cm) of quadrilateral PQRS?
Options- A. (64√3)/3
- B. (177√3)/2
- C. (135√3)/2
- D. (98√3)/3 Discuss
Correct Answer: (135√3)/2
- 7. PQR is a triangle, whose area is 180 cm2. S is a point on side QR, such that PS is the angle bisector of ?QPR. If PQ : PR = 2 : 3, then what is the area (in cm2) triangle PSR?
Options- A. 90
- B. 108
- C. 144
- D. 72 Discuss
Correct Answer: 108
- 8. In the given figure, ABCD is a square. EFGH is a square formed by joining mid points of sides of ABCD. LMNO is a square formed by joining mid points of sides of EFGH. A circle is inscribed inside EFGH. If area of circle is 38.5 sq.cm, the what is the area (in sq.cm) of square ABCD?
Options- A. 98
- B. 196
- C. 122.5
- D. 171.5 Discuss
Correct Answer: 196
- 9. In the given figure, PQRS is a rectangle and a semicircle with SR as diameter is drawn. A circle is drawn as shown in the figure. If QR = 7 cm, then what is the radius (in cm) of the small circle?
Options- A. 21+14√2
- B. 21-14√2
- C. 20+14√2
- D. 20-14√2 Discuss
Correct Answer: 21-14√2
- 10. In the given figure, PQR is a quadrant whose radius is 7 cm. A circle is inscribed in the quadrant as shown in the figure. What is the area (in sq.cm) of the circle?
Options- A. 385-221√2
- B. 308-154√2
- C. 154-77√2
- D. 462-308√2 Discuss
Correct Answer: 462-308√2
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