(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 (pi = frac{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 three significant figures, the distance between X and Y along latitude 28°N ; (ii) How far is X from the equator? [Take (pi = frac{22}{7}) and radius of the earth = 6,400km].
Explanation
(a) (d = 15 cm implies r = frac{15}{2} cm)
(V = frac{4pi r^{3}}{3})
(V = frac{4}{3} times frac{22}{7} times (frac{15}{2})^{3})
(V = frac{1125 times 22}{7 times 2})
(V = 1,767.857 cm^{3})
(b)(i) Longitude difference : 105° + 35° = 140°
Distance along the parallel of latitude = (frac{140}{360} times 2 times frac{22}{7} times 6400 cos 28)
= (frac{140 times 44 times 6400 times 0.8829}{360 times 7})
= (13812.48 km)
(approxeq 13800 km)
(ii) Distance from the equator : (frac{28}{360} times 2 times frac{22}{7} times 6400)
= (3128.89 km)
(approxeq 3130 km)