Question

13(a) The diameter of a cylinder closed at both ends is 7cm. If the total surface area is 209cm², 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.

Accepted Answer

(a) Radius r=3.5cm. Total surface area (closed cylinder) = 2πr²+2πrh.
209 = 2×(22/7)×(3.5)² + 2×(22/7)×3.5×h
209 = 77 + 22h
132 = 22h
h = 6cm.

(b)(i) [Diagram: T at top of tree, X and Y on the ground 19m apart, with angle of elevation 43° from X (closer) and 38° from Y (farther), foot of tree at point between/beyond X.]

(ii) Let the height of tree = h, and let x = distance from X to the foot of the tree.
tan43° = h/x ⟹ h = x·tan43° ...(1)
tan38° = h/(x+19) ⟹ h = (x+19)tan38° ...(2)
Equating (1) and (2): x·tan43° = (x+19)tan38°
x(0.9325) = (x+19)(0.7813)
0.9325x = 0.7813x+14.845
0.1512x = 14.845
x = 98.17m
h = 98.17×tan43° = 98.17×0.9325 = 91.6m.

WAEC Mathematics 2022 Theory — Question 13

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