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Volume and Surface Area problems

  • 1. ABCD is a cyclic trapezium in which AD || BC. If ?ABC = 70°, then ?BCD is

  • Options
  • A. 110°
  • B. 80°
  • C. 70°
  • D. 90°
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  • 2. G is the centroid of ?ABC. If AG = BC, then measure of ?BGC is

  • Options
  • A. 45°
  • B. 60°
  • C. 90°
  • D. 120°
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  • 3. In a circle, a chord, 5?2 cm long, makes a right angle at the centre. Then the length of the radius of the circle will be

  • Options
  • A. 2.5 cm
  • B. 5 cm
  • C. 7.5 cm
  • D. 10 cm
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  • 4. Thousand solid metallic spheres of diameter 6 cm are melted and recast into a new solid sphere. The diameter of the new sphere (in cm) is

  • Options
  • A. 30
  • B. 90
  • C. 45
  • D. 60
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  • 5. In ?ABC , DE || AC. Where D and E are two points lying on AB and BC respectively. If AB = 5 cm and AD = 3 cm, then BE : EC is

  • Options
  • A. 2:3
  • B. 3:2
  • C. 5:3
  • D. 3:5
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  • 6. PT is a tangent to a circle with centre O and radius 6 cm . If PT is 8 cm then length of OP is

  • Options
  • A. 10 cm
  • B. 12 cm
  • C. 16 cm
  • D. 9 cm
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  • 7. D, E, F are the mid - points of the sides BC , CA and AB respectively of a ?ABC . Then the ratio of the areas of ?DEF and ?ABC is

  • Options
  • A. 1/2
  • B. 1/4
  • C. 1/8
  • D. 1/16
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  • 8. A circle has its centre at O . A tangent drawn from a point P , which is situated outside the circle, touches the circle at A. If PA = 4 cm & PO=5 cm, then the length of the radius of the circle is

  • Options
  • A. 1 cm
  • B. 2 cm
  • C. 3 cm
  • D. 4 cm
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  • 9. An inverted conical shaped vessel is filled with water to its brim. The height of the vessel is 8 cm and radius of the open end is 5 cm . When a few solid spherical metallic balls each of radius 1?2 cm are dropped in the vessel , 25% water is overflowed. The number of balls is:

  • Options
  • A. 100
  • B. 400
  • C. 200
  • D. 150
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  • 10. Number of circles that can be drawn through three non-colinear points is

  • Options
  • A. exactly one
  • B. two
  • C. three
  • D. more than three
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