Question

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

• A. $700c{m}^2$
• B. $781.86c{m}^2$
  
• C. $724.25c{m}^2$
• D. $525.25c{m}^2$

Answer 1

The correct option is B $781.86c{m}^2$

Curved surface area of cylinder
$2\pi rh=\pi \times 8\times 10=80\times \pi$

The slant height of frustum can be calculated as follows:
$l=\sqrt{h^2+(r_1-r_2{)}^2}=\sqrt{{12}^2+(9-4{)}^2}=\sqrt{144+25}=\sqrt{169}=13cm$

Curved surface area of frustum
$=\pi (r_1+r_2)l=\pi (9+4)\times 13=169\pi$

Total curved surface area
$=169\pi +80\pi =249\times 3.14=781.86c{m}^2$