Question

a solid cylinder has a total surface area 462 sq.cm.its curved surface area is one-third the total surface area.find the volume of the cylinder.

Answer 1

 Let the radius and height of the cylinder be r cm and h cm respectively.
Given, Total surface area of the cylinder = 462 cm2∴ 2p r (r + h) = 462 cm2       .. .(1)Lateral surface area of cylinder =  1/3 × Total surface area of cylinder
 (Given)∴ 2prh =1/3 × 462 = 154 cm2 ... (2)
From (1) and (2), we have{2pr(r+h}/{2pr} = 462 cm2       / 154 cm2(r+h) / h = 3r = 3h-h=2hr = 2hFrom (2), we have2prh =154 cm2(2 x22rxr) /(7x2)}r = 7cmh = r/2=7/2=3.5cm
∴ Volume of the cylinder  = pr2h =22x7x7/3.5=539 cm3

Answer 2

TSA of cylinder=2×22/7×r(h+r)
2×22/7×r(h+r)=462
rh+r²=73.5
csa=1/3×462=154
2×22/7×r×h=154
rh=24.5
24.5+r²=73.5
r²=49
r=7 cm
rh=24.5
7h=24.5
h=3.5 cm
volume=22/7×r²×h
22/7×49×3.5
3773/7
=539 cm³