Let radii of the circular ends of the frustum are R and r respectively.
Given that Perimeter of one end = 96cm
⇒ 2πR = 96
⇒ 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]
= 22/7 x 884.83
= 2780.89 cm2