(a) The diameter of a cylinder closed at both ends is 7cm. If the total surface area is 209cm2 2 , calculate the height. [Take pi = 22/7]. (b) The points X ...

(a) The diameter of a cylinder closed at both ends is 7cm. If the total surface area is 209cm2 ${}^2$, 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.

Answer Details

209 = 2 * 227 $\frac{\mathrm{<br>}}{}$ * (72)2 $<br>{\mathrm{<br>}}^{}$ + 2 * 227 $\frac{\mathrm{<br>}}{}$ * 72 $\frac{\mathrm{<br>}}{}$ * h

209 = 77 + 22h

132 = 22h

h = 6cm

(b) tan 43º = hy $\frac{\mathrm{<br>}}{}$

0.9125y = h ...[i]

tan 38º = hy+19 $\frac{\mathrm{<br>}}{}$

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