Question

The perimeter of end of the frustum of a cone are 207. 24 centimetre and 169.5 CM if the height of the frustum be 8cm. Find the whole surface area of frustum

Answer 1

first we would need to find the radius of the upper and lower face of the frustum
let the greater radius be R and the smaller be R

perimeter of small circle = 2pir
169.5= 2+22/7×r
169.5-2= 22/7×r
( 167.5×7)/22=r
1172.5/22=r
53.3 cm =r

perimeter of big circle=2piR
207.4=2×22/7×R
(205.4×7)/22=R
( 102.7×7 )/11=R
718.9/11=R
65.3cm=R

l=root h^2+(R-r)^2
=root 8^2+(65.3-53.3)^2
=root 64 +(12)^2
= root 64+144
=root 208


TSA of frustum=pi{R^2+r^2+l(R+r)}
=22/7{65.5^2+53.3^2+root 208(65.3+53.3)}
=22/7{4264.09+2840.89+root 208(118.6)}
=22/7{7104.98+ 118.6root208}
=22{1015+118.6root208}
=22330+2609.2root208 cm^2