(a) The diameter of a cylinder closed at both ends is 7cm. If the total surface area is 209cm\(^2\), calculate the height. [Take pi = 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 43º and 38° respectively.
(i) Illustrate the information in a diagram. (ii) Find, correct to one decimal place, the height of the tree.
Explanation
209 = 2 * \(\frac{22}{7}\) * \((\frac{7}{2})^2\) + 2 * \(\frac{22}{7}\) * \(\frac{7}{2}\) * h
209 = 77 + 22h
132 = 22h
h = 6cm
(b) tan 43º = \(\frac{h}{y}\)
0.9125y = h ...[i]
tan 38º = \(\frac{h}{y+19}\)
0.7813(y+19) = h ...[ii]
0.7813(y+19) = 0.9125y
0.7813y + 14.8447 = 0.93257
14.8447 = 0.1512y
y= 98.1792
= 98.2m
h = 0.9325 x 98.1792
= 91.55
=91.6m