Question

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

Answer 1

please see pictures given below

Answer 2

Answer:

781.86 sq.cm.

Step-by-step explanation:

Height of cylinder = 10 cm

Radius of cylinder = $\frac{\text{Diameter of cylinder}}{2}=\frac{8}{2}=4 cm$

Curved surface area of cylinder = $2 \pi r h$

                                                     = $2 \times 3.14 \times 4 \times 10$

                                                     = $251.2 cm^2$

Total height of funnel = 22 cm

Height of frustum = Total height - Height of cylinder

Height of frustum = 22 cm - 10 cm = 12 cm

Radius of top of funnel or radius of one end of frustum  = $\frac{18}{2}=9 cm$

Radius of other end of frustum = 4 cm

Curved surface area of frustum = $\pi (r+R)\sqrt{(R-r)^2+h^2}$

                                                    = $3.14 (4+9)\sqrt{(9-4)^2+12^2}$

                                                    = $530.66 cm^2$

Total curved surface area of frustum = 251.2 + 530.66=781.86 sq.cm.

Hence  the area of the sheet required to make funnel is 781.86 sq.cm.