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, diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel (see Fig. 13.25)
Solution:
Since the funnel is open at the top and the bottom hence, it is open at the junction of the frustum of cone and cylindrical part.
Therefore,
Area of tin sheet required to make the funnel = CSA of frustum of cone + CSA of the cylinder
We will find the CSA of the frustum by using formulae;
CSA of frustum of a cone = π (r₁ + r₂)l
Slant height, l = h² + (r₁ - r₂)²
where r₁, r₂, h and l are the radii height and slant height of the frustum of the cone respectively.
CSA of the cylinder = 2πrh
where r and h are radius and height of the cylinder respectively.
Height of the funnel, H = 22 cm
Height of cylindrical part, h = 10 cm
Height of frustum of cone, h₁ = 22 cm - 10 cm = 12 cm
Radius of top part of frustum of cone, r₁ = 18/2 cm = 9 cm
Radius of lower part of frustum of cone, r₂ = 8/2 cm = 4 cm
Radius of cylindrical part, r₂ = 4 cm
Slant height of frustum, l = √h₁² + (r₁ - r₂)²
= √(12 cm)² + (9 cm - 4 cm)²
= √144 cm² + 25 cm²
= √169 cm²
= 13 cm
Area of tin sheet required to make the funnel = CSA of frustum of cone + CSA of the cylinder
= π (r₁ + r₂)l + 2πr₂h
= π[(r₁ + r₂)l + 2r₂h]
= 22/7 [(9 cm + 4 cm) × 13 cm + 2 × 4 cm × 10 cm]
= 22/7 [169 cm² + 80 cm²]
= 22/7 × 249 cm²
= 5478/7 cm²
= 782.57 cm²
☛ Check: NCERT Solutions for Class 10 Maths Chapter 13
Video Solution:
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, diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel.
NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 Question 5
Summary:
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, diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, the area of the tin sheet required to make the funnel is 782.57 cm².
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