Theory question 113
Mensuration of Solids(a) A boy blew his rubber balloon to a spherical shape. The balloon burst when its diameter was 15 cm. Calculate, correct to the nearest whole number, the volume of air in the balloon at the point of bursting. [Take π = 22/7].
(b) A point X is on latitude 28°N and longitude 105°W. Y is another point on the same latitude as X but on longitude 35°E. (i) Calculate, correct to 3 significant figures, the distance between X and Y along latitude 28°N. (ii) How far is X from the equator? [Take π = 22/7, and the radius of the Earth as 6,400 km]
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(a) r = 7.5 cm: V = 4/3 × 22/7 × 7.53 ≈ 1768 cm3.
(b)(i) Difference in longitude = 105 + 35 = 140°. Radius of the latitude circle = 6400 cos 28°.
Distance = 140/360 × 2 × 22/7 × 6400 × cos 28° ≈ 15644 × 0.8829 ≈ 13,800 km.
(ii) Along the meridian: 28/360 × 2 × 22/7 × 6400 ≈ 3,130 km.
One point is west and the other east of Greenwich, so add the longitudes.