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Volume and Surface Area problems


  • 1. If the diameter of a hemisphere is 21 cm, then what is the volume (in cub.cm) of hemisphere?

  • Options
  • A. 2810
  • B. 1250.5
  • C. 1725.25
  • D. 2425.5
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  • 2. In ?ABC, AD is the median and AD = (1/2)BC. If ?ACD = 40°, then what is the value (in degrees) of ?DAB?

  • Options
  • A. 30
  • B. 40
  • C. 50
  • D. 60
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  • 3. Circum center of ?ABC is O. If ?BAC = 75 and ?BCA = 80 degrees, then what is the value of ?OAC(in deg)?

  • Options
  • A. 45
  • B. 65
  • C. 90
  • D. 95
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  • 4. The ratio of the volume of two cylinders is 7 : 3 and the ratio of their heights is 7 : 9. If the area of the base of the second cylinder is 154 sq. cm, then what will be the radius (in cm) of the first cylinder?

  • Options
  • A. 6?2
  • B. 6?3
  • C. 7?2
  • D. 7?3
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  • 5. In triangle ABC, AD, BE and CF are the medians intersecting at point G and area of triangle ABC is 156 sq.cm. What is the area (in sq.cm) of triangle FGE?

  • Options
  • A. 13
  • B. 26
  • C. 39
  • D. 52
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  • 6. The length of diagonal of a square is 9?2 cm. The square is reshaped to form a triangle. What is the area (in sq.cm) of largest in circle that can be formed in that triangle?

  • Options
  • A. 6?
  • B. 9?
  • C. 12?
  • D. 15?
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  • 7. If the radius of the cylinder is increased by 25%, then by how much percent the height must be reduced, so that the volume of the cylinder remains same?

  • Options
  • A. 36
  • B. 56
  • C. 64
  • D. 46
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  • 8. In ?ABC, ?BAC = 90° and AD is drawn perpendicular to BC. If BD = 7 cm and CD = 28 cm, then what is the length (in cm) of AD?

  • Options
  • A. 3.5
  • B. 7
  • C. 10.5
  • D. 14
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  • 9. A chord of length 60 cm is at a distance of 16 cm from the centre of a circle. What is the radius (in cm) of the circle?

  • Options
  • A. 17
  • B. 34
  • C. 51
  • D. 68
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  • 10. T is a point on the common tangents at P of two circles and if TA and TB are resectively the other tangents at A and B to the two circles drawn from the point T then

  • Options
  • A. TA = 2 TB
  • B. TA = TB
  • C. TA = 1/2 TB
  • D. 3TA = TB
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