Theory question 113
Mensuration of Solids(a) The diameter of a cylinder closed at both ends is 7cm. If the total surface area is 209 cm2, calculate the height. [Take π = 22/7]
(b) The points X and Y, 19m apart are on the same side of a tree. The angles of elevation of the top, T, of the tree from X and Y on the horizontal ground with the foot of the tree are 43° and 38° respectively. (i) Illustrate the information in a diagram. (ii) Find, correct to one decimal place, the height of the tree.
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(a) r = 3.5 cm; TSA = 2πr(r + h) = 2 × (22/7) × 3.5 × (3.5 + h) = 22(3.5 + h)
22(3.5 + h) = 209 → 3.5 + h = 9.5 → h = 6 cm
(b)(i) Tree TB vertical; X nearer (43°), Y 19 m further away (38°), all on a line with B
(ii) Let XB = d, height h: h = d tan 43° = (d + 19) tan 38°
d(tan 43° − tan 38°) = 19 tan 38° → d ≈ 98.2 m
h = 98.2 × tan 43° ≈ 91.5 m
The larger angle of elevation belongs to the point nearer the tree.