Question

An oil funnel of tin sheet consists of a cylindrical portion $10cm$ long attached to a frustum of a cone. If the total height be $22cm$, diameter of the cylindrical portion be $8cm$ and the diameter of the top of the funnel be $18cm$, find the area of the tin required to make the funnel.

• A. $876.26c{m}^2$
• B. $657.26c{m}^2$
• C. $782.57c{m}^2$
• D. $982.26c{m}^2$

Answer 1

The correct option is C $782.57c{m}^2$

Let $l$ be the slant height of the frustum part of the funnel.

Then,

$l=\sqrt{{(r_1-r_2)}^2+h^2}$

$l=\sqrt{(9-4{)}^2+{12}^2}=13cm$

Now,

Tin required=Curved surface area of cylinder portion + Curved surface area of frustum portion

Tin required $=2\pi r_{1}h+\pi (r_1+r_2)l$

$=\{2\pi \times 4\times 10+\pi (4+9)\times 13\}=249\pi c{m}^2$

Area of Tin required $=782.57c{m}^2$