Q4 of 44 Page 15

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]


Let radii of the circular ends of the frustum are R and r respectively.


Given that Perimeter of one end = 96cm


⇒ 2πR = 96




⇒ R = 15.27 cm


Perimeter of other end = 68cm


⇒ 2πr = 68




⇒ r = 10.82 cm


It is given that height of the frustum = 20cm


So, Slant height, l = √{h2 + (R – r)2}


= √{(20)2 +(15.27 – 10.82)2


= √400 + (4.45)2


= √400 + 19.80


= √419.80


= 20.49 cm


Now,






= 10800.25 cm3


Total Surface Area of the frustum = πR2 + πr2 + πl(R+r)


= π[(15.27)2 + (10.82)2+ 20.49×(15.27+10.82)]


= π[233.1729 + 117.0724 + 534.5841]



= 2780.89 cm2


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