Theory question 107
Mensuration of Solids(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 m. Caculate, correct to three significant figures, the surface area of the structure. [Take π = 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.
Show the model answer
(a) Slant height l = √(482 + 142) = √2500 = 50 m
Curved surface of cone = πrl = (22/7) × 14 × 50 = 2200 m2
Curved surface of hemisphere = 2πr2 = 2 × (22/7) × 196 = 1232 m2
Total = 3432 ≈ 3430 m2 (3 s.f.)
(b) M + S = 100 and M − 5 = 2(S − 5) → M = 2S − 5
3S − 5 = 100 → S = 35
Sesay is 35 years old
The flat circle where the cone sits on the hemisphere is hidden, so it is not part of the surface.