(a) Without using tables, find the value of (frac{0.45 times 0.91}{0.0117})
(b) Find the number which is exactly halfway between (1frac{6}{7}) and (2frac{11}{28}).
(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 (pi = frac{22}{7})].
Explanation
(a) (frac{0.45 times 0.91}{0.0117} = frac{45 times 91}{117})
= (5 times 7 = 35)
(b) Halfway between (1frac{6}{7}) and (2frac{11}{28})
= (frac{1frac{6}{7} + 2frac{11}{28}}{2})
= ((frac{13}{7} + frac{67}{28}) times frac{1}{2})
= (frac{119}{28} times frac{1}{2} )
= (frac{119}{56} = 2frac{7}{56} = 2frac{1}{8})
(c) Let the interior angle = 5x° and the exterior angle = x°.
(therefore 5x° + x° = 180°)
(6x° = 180° implies x = 30°)
Exterior angle = (frac{360°}{n} implies 30° = frac{360°}{n})
(n = frac{360°}{30°} = 12)
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
(therefore) Volume of material used = (pi R^{2} l – pi r^{2} l)
Where l = length.
(Volume = pi l (R^{2} – r^{2}) cm^{3})
= (frac{22}{7} times 20 (4^{2} – 3^{2}) = frac{22}{7} times 20 times 7 = 440 cm^{3})