(a) Without using tables, find the value of (b) Find the number which is exactly halfway between and . (c) If each interior angle of a regular polygon is five times the exterior angle, how many sides has the polygon? (d) Calculate the volume of the material used in making a pipe 20cm long, with an internal diameter 6cm and external diameter 8cm. [Take ].
Explanation
(a) = (b) Halfway between and = = = = (c) Let the interior angle = 5x° and the exterior angle = x°. Exterior angle = The polygon has 12 sides. (d) Length of pipe = 20 cm Internal diameter = 6 cm ; radius = 3cm External diameter = 8 cm ; radius = 4cm Let the external radius = R and internal radius = r Volume of material used = Where l = length. =