ABSTRACT
Determine (a) the diameter of the circle, and (b) the co-ordinates of the centre of the circle. (5)
10. Determine the volume (in cubic metres) and the total surface area (in square metres) of a solid metal cone of base radius 0.5 m and perpendicular height 1.20 m. Give answers correct to 2 decimal places. (5)
11. Calculate the total surface area of a 10 cm by 15 cm rectangular pyramid of height 20 cm. (5)
12. A water container is of the form of a central cylindrical part 3.0 m long and diameter 1.0 m, with a hemispherical section surmounted at each end as shown in Fig. RT5.4. Determine the maximum capacity of the container, correct to the nearest litre. (1 litre=1000 cm3.) (5)
13. Find surface area con-of an inverted of slant height 35.0 cm and end diameters 60.0 cm and 40.0 cm. (4)
14. A boat has a mass of 20 000 kg. A model of the boat is made to a scale of 1 to 80. If the model is made of the same material as the boat, determine the mass of the model (in grams). (3)
15. Plot a graph of y =3x2 +5 from x =1 to x =4. Estimate, correct to 2 decimal places, using 6 intervals, the area enclosed by the curve, the ordinates x =1 and x =4, and the x-axis by
(a) the and (c)
16. A vehicle starts from rest and its velocity is measured every second for 6 seconds, with the following results:
Time t (s) 0 1 2 3 4 5 6 Velocity v (m/s) 0 1.2 2.4 3.7 5.2 6.0 9.2
Using Simpson’s rule, calculate (a) the distance travelled in 6 s (i.e. the area under the v/t graph) and (b) the average speed over this period. (6)
For lecturers/instructors/teachers, fully worked solutions to each of the problems in Revision Test 5, together with a full marking scheme, are available at the website:
