Q5 of 44 Page 15

A friction clutch in the form of the frustum of a cone, the diameters of the ends being 8cm, and 10 cm and length 8 cm. Find its bearing surface and its volume. [Take π=3.14]


We have,


Diameter of one end = 10cm


So, radius (R) = 5cm


Diameter of other end = 8cm


So, radius (r) = 4cm


and slant height, l = 8cm


So, height, h = √{l2 – (R – r)2}


= √{(8)2 – (5 – 4)2


= √64 – (1)2


= √64 – 1


= √63


= 7.937 cm


Bearing surface of the clutch = CSA of the frustum


= πl (R + r)


= 3.14 × 8 (5 + 4)


= 25.12 (9)


= 226.08 cm2






= 506.75 cm3


Hence, Volume of frustum = 506.75 cm3


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3

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 4

The perimeters of the ends of the frustum of a cone are 96 cm and 68 cm. If the height of the frustum be 20 cm, find its radii, slant height, volume and total surface. [Take π=22/7]

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An open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet (see Fig.) The diameters of the two circular ends of the bucket are 45 cm and 25cm, the total vertical height of the bucket is 40cm and that of the cylindrical base is 6cm. Find the area of the metallic sheet used to make the bucket, where we do not take into account the handle of the bucket. Also, find the volume of water the bucket can hold. [Take π=22/7]