WAEC Mathematics 2020 Theory — Question 7

Model answer

Surface area of the structure = Curved surface area of the cone + Curved surface area of the hemisphere = pi*r*l + 2*pi*r^2 = pi*r(l+2r). To find l, use Pythagoras: l^2=48^2+14^2=2304+196=2500, so l=50m. Surface area = (22/7)*14*(50+2(14)) = 22*2*(50+28) = 44*78 = 3432 cm^2, which rounds to 3430 cm^2 (to 3 s.f). (b) The sum of the present ages of Sesay and Musah is 100 years. Five years ago, Musah's age was two times Sesay's age. Find their present ages. Let Sesay's age be x, Musah's age be y. x+y=100 ...(i). Five years ago: Musah's age = y-5, Sesay's age = x-5. Also, y-5=2(x-5), i.e. y-5=2x-10, so y=2x-5 ...(ii). Substituting (ii) into (i): x+(2x-5)=100 => 3x-5=100 => 3x=105 => x=35. Then y=100-35=65. Therefore, Sesay's age = 35 years, Musah's age = 65 years.