(a) The diagram shows a wooden structure in the form of a cone, mounted on...
(a) The diagram shows a wooden structure in the form of a cone, mounted on a hemispherical base. The vertical height of the cone is 48 m and the base radius is 14. Calculate, correct to three significant figures, the surface area of the structure, [Take \(\pi = \frac{22}{7}\)]
(b) Five years ago, Musah was twice as old as Sesay. If the sum of their ages is 100, find Sesay's present age.
Explanation
Surface Area = \(\pi^2 + \pi rl + 2 \pi r^2\)
\(\frac{22}{7}\) x 14 x 14 + \(\frac{22}{7}\) x 14 x 50 + 2 x \(\frac{22}{7}\) x 14 x 14
l\(^2\) = 48\(^2\) + 14\(^2\)
l\(^2\) = 2500
l = \(\sqrt{2500}\) = 50
l = 616 + 2,200 + 1,232
= \(\sqrt{4048}\)
= 63.62m\(^2\)
(b) Let Musah age be M
Let Sesay be S
M - 5 = 2(S - 5) ......(i)
M + S = 100 ......(ii)
2(S - 5) +(S - 5) = 100
3S - 15 = 100
3S = 100 + 15
\(\frac{3S}{3} = \frac{115}{3}\)
S = 38.33years
Sesay is 35 years