Source: Complete International Mathematics For Cambridge IGCSE - David Rayner, Jim Fenson

1. Water is flowing into an inverted cone of diameter and height 30 cm,
    at a rate of 4 liters per minute.
    How long in seconds, will it take to fill the cone?


2. A spherical ball is immersed in water contained in a vertical cylinder.
    The rise in water level is measured in order to calculate the radius of the spherical balls.
    Calculate the radius of the balls in the following cases:
a) Cylinder of radius 10 cm, water level rises 4 cm
b) Cylinder of radius 100 cm, water level rises 8 cm.


3. One corner of a solid cube of side 8 cm is removed by cutting through the midpoints of 
    three adjacent sides. 
    Calculate the volume of the piece removed.

4. The cylindrical end of a pencil is sharpened to produce a perfect cone at the end with no 
    overall loss of length. If the diameter of the pencil is 1 cm, and the cone is of length 2 cm, 
   calculate the volume of the shavings.


5. An inverted cone of height 12 cm and base radius 6 cm contains 20 cm³ of water.
   Calculate the depth of water in the cone, measured from the vertex.


6. A frustum is a cone with 'the end chopped off'. 
    A bucket in the shape of a frustum as shown has diameters of 10 cm and 4 cm
    at its ends and a depth of 3 cm.     
   Calculate the volume of the bucket.

  The volume of the bucket(frustum) is basically the
volume of cut off portion of cone subtracted from
volume of entire cone.

7. The diagram shows a sector of a circle of radius 10 cm.

    a) Find as a multiple of π, the arc length of the sector.
    The straight edges are brought together to make a cone. Calculate:
    b) the radius of the base of the cone,
    c) the vertical height of the cone.

 b)Circumference of the base of cone is the arc length of sector of circle.

8. A sphere passes through the eight corners of a cube of side 10 cm.
    Find the volume of the sphere.



9. Find the volume of a tetrahedron of side 20 cm.
    (A regular tetrahedron has four equal faces which are equilateral triangle)

 Plan of the base of tetrahedron.

Back to top