(a) A cylindrical pipe is 28 metres long. Its internal radius is 3.5 cm and external radius 5 cm. Calaulate : (i) the volume, in cm, of metal used in making the pipe ; (ii) the volume of water in litres that the pipe can hold when full, correct to 1 decimal place. [Take ] (b) In the diagram, MP is a tangent to the circle LMN at M. If the chord LN is parallel to MP, show that the triangle LMN is isosceles.
Explanation
(a)(i) Volume of outer pipe = = Volume of inner pipe = Volume of metal used = Volume of outer pipe - Volume of inner pipe = = = (ii) Vol of water the pipe can hold = vol of inner pipe = = = 107.8 litres. (b) < PMN = < LNM (alternate angles) < PMN = < LMN (angles in alternate segment) < LNM = < NLM, then LMN is isosceles.
