Question

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

Answer 1

Given: Total height of the funnel = 22 cm

For Cylindrical Portion:

Height (h₁) = 10 cm

Radius (r₂) = `"Diameter"/2` = `8/2` = 4 cm

For Frustum of a Cone:

Height (h₂) = Total height − h₁

= 22 – 10

= 12 cm

Top radius (r₁) = `"Top diameter"/2`

= `18/2`

= 9 cm

Bottom radius = Same as the cylinder radius (r₂) = 4 cm

1. Finding Slant Height of Frustum (l):

`l = sqrt(h_2^2 + (r_1 - r_2)^2`

= `sqrt(12^2 + (9 - 4)^2`

= `sqrt(144 + 5^2)` 

= `sqrt(144 + 25)`

= `sqrt(169)`

= 13 cm

2. Finding Total Area of Tin Sheet Required:

Total Area = Curved Surface Area of Cylinder + Curved Surface Area of Frustum

Total Area = 2πr₂h₁ + π(r₁ + r₂)l

= (2 × π × 4 × 10) + [π × (9 + 4) × 13]

= 80π + (13 × 13π)

= 80π + 169π

= 249π

Using π = `22/7`:

Total Area = `249 xx 22/7`

= `5478/7`

≈ 782.57 cm²