1. (a) A cone and a pyramid have equal heights and volumes. If the base area of the pyramid is 154cm?, find the radius of the cone. (Take 7 = 2)
(b) A spherical bowl of radius rcm is a quarter full when 6 litres of water is poured into it.
Calculate, correct to three
signifcant figures, the diameter of the bowl. (Take 1 = 21.
2. Each of a group of 20 students studies at least one of the three subjects, Chemistry, Physics and
Biology. All those who study Physics also study Chemistry, 3 students study all three subjects. 4
students study only Chemistry, 8 students study Physics, 14 students study Chemistry.
(a) Draw a Venn diagram to illustrate the information.
(b) How many students study Chemistry and Biology but not Physics?
Pc
(c) What is the probability that a student selected at random from the group studies only
Biology?
3. (a) In the diagram below P, Q, R and S are points on the circumference of a circle with centre
0. PUT = |SU), PR] = |SQI, angle PTS = 30° and angle QPU = 35°.