Question

A funnel of tin sheet consists of a cylindrical portion, $10cm$ long, attached to a frustum of a cone. If a diameter of the top and bottom of the frustum is $18cm$ and $8cm$ respectively and the slant height of the frustum of cone is $13cm$, find the surface area of the tin required to make the funnel.

Answer 1

We know $\frac{EC}{EB}=\frac{OD}{KA}$ (Similar triangle)

$\frac{x}{x+13}=\frac{4}{9}$

$\Rightarrow 9x=4x+52$

$\Rightarrow 5x=52$

$\Rightarrow x=10.4$

Surface area of cone $=\pi r(r+l)$

where $r$ is radius and $l$ is slant height

So, surface area of conical part $=$ Surface area of bigger cone $-$ Surface area of small imaginary cone

$=\pi \times 9\times (9+(13+10.4\left)\right)-\pi \times 9\times (4+10.4)$

$=\pi \times 234$

Surface area of cylindrical part $=2\pi rh$

$=2\times \pi \times 4\times 10$

$=80\pi$

So, total surface area $=234\pi +80\pi$

$=314\pi$ sq. units