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.) .

Ncert solutions class 10 chapter 13-36

Given

Larger radius of frustum (R) = 18/2 = 9 cm

Smaller radius of frustum (r) = 8/2 = 4 cm

Height of frustum (H) = 22-10 = 12 cm

Radius of cylinder (r) = 8/2= 4 cm

Height of cylinder (h) = 10 cm

Solution

Area of the tin sheet required = CSA of frustum + CSA of cylinder

CSA of frustum = π(r+R)l

(l =√(H2 + (R-r)2))

l=√(122 + (9-4)2)

 l = 13 cm

CSA of frustum = π(r+R)l

π×(9+4)×13

π×13×13

= 169π cm2

CSA of cylinder = 2πrh

2×π×4×10

= 80π cm2

Area of the tin sheet required = 169π + 80π

= 249π

Now let us consider π=22/7

= 782.571 cm2

 Answer

the area of the tin sheet required to make the funnel is 782.571 cm2

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