Question

The flask consist of a cylindrical part and a frustum of a cone. The diameter of the base is 10 cm the diameter is 2 cm while that of neck is 2 cm. The vertical height of the flask is 12 cm.
(a) the slant height of the frustum part;
(b) the slant height of the smaller cone that was cut off to make the frustum part.
(c) the external surface area of the flask. (Take pi = 3.142)

Answer 1

Consider the cut-off part of the cone. If the height of the frustrum is 4x, then since the radius shrinks from 5 to 1, using similar triangles, the missing top part has height x.

thus, the volume of the missing part is 1π/3 * 1^2 x = π/3 x
The volume of the frustrum is thus π/3 (5^2*5x - 1^2 x) = 8πx

(a) s1^2 = (4x)^2+(5-1)^2
(b) s2^2 = x^2+1^2
(c) a = π*5^2*(12-x) + 2π*5*s1 - 2π*1*s2

Answer 2

Height = 12 - 2
= 10
Cylindrical part = 12 - 2
= 2