ABSTRACT
Fig. A10.1. The section of the groove is a semicircle of diameter 50 mm. Given that the centroid of a semicircle from its base is
4r 3π
, use the theorem of Pappus to determine the volume of material removed, in cm3, correct to 3 significant figures. (8)
8. A circular door is hinged so that it turns about a tangent. If its diameter is 1.0 m find its second moment of area and radius of gyration about the hinge. (5)
9. Determine the following integrals:
(a) ∫
5(6t + 5)7 dt (b) ∫ 3 ln x
x dx
(c) ∫ 2√(2θ − 1) dθ (9)
10. Evaluate the following definite integrals:
(a) ∫ π
0 2 sin
( 2t + π
) dt (b)
(10)
