Theory question 106
Fractions, Decimals and ApproximationPART II. (a) Without using tables, find the value of (0.45 × 0.91)/0.0117 (b) Find the number which is exactly half way between 1 6/7 and 2 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 π = 22/7].
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(a) (0.45 × 0.91)/0.0117 = (45 × 91)/117 = (45 × 91)/(9 × 13) = 5 × 7 = 35.
(b) 1 6/7 = 52/28 and 2 11/28 = 67/28. Half way = (52/28 + 67/28) ÷ 2 = 119/56 = 2 1/8.
(c) Let the exterior angle be x; then 5x + x = 180°, so x = 30°. Number of sides = 360° ÷ 30° = 12.
(d) External radius 4 cm, internal radius 3 cm. Volume = π(R2 − r2)h = 22/7 × (16 − 9) × 20 = 22/7 × 7 × 20 = 440 cm3.
In (d) the material is the outer cylinder minus the hollow inner cylinder.