(a) A cylindrical well of radius 1 metre is dug out to a depth of 8 metres. (i) calculate, in m, the volume of soil dug out ; (ii) if the soil is used to raise the level of rectangular floor of a room 4m by 12m, calculate, correct to the nearest cm, the thickness of the new layer of soil. [Take ]. (b) The diagram shows a quadrilateral ABCD in which < DAB is a right- angle. |AB| = 3.3 cm, |BC| = 3.9 cm, |CD| = 5.6 cm. (i) find the length of BD. (ii) show that < BCD = 90°.
Explanation
(a) (i) r = 1m, h = 8m. = = (ii) = (nearest whole number) (b)(i) = = (ii) If < BCD is right- angled, then Pythagoras rule holds true. = Hence, is right-angled.