Question

4(a) The ratio of the radius to the slant height of a right circular cone is 2:5. If the total surface area of the cone is 224*pi cm^2, calculate: (i) slant height; (ii) volume of the cone. [Take pi=22/7]

Accepted Answer

(a)(i) Given r:l = 2:5, so r/l=2/5, meaning l=5r/2. Total surface area of a cone = pi*rl + pi*r^2 = 224*pi cm^2 (i.e. rl+r^2=224). Substituting l=5r/2: r(5r/2)+r^2=224 => (5r^2/2)+r^2=224 => (7r^2/2)=224 => r^2=64 => r=8cm. Then l=5(8)/2=20cm.
(ii) To find the volume, we need the height h, using Pythagoras: h^2=l^2-r^2=20^2-8^2=400-64=336, so h=sqrt336=18.33cm. Volume=(1/3)*pi*r^2*h=(1/3)(22/7)(8^2)(18.33)=1228.98 cm^3.

WAEC Mathematics 2020 Theory — Question 4

Sign up free to unlock