The total surface area of a hollow cylinder which is open from both sides is 4620 sq. cm, area of base ring is 115.5 sq. cm, and height is 7 cm. Find the thickness of the cylinder.
Let the inner and outer radii of hollow cylinder be r cm and R cm respectively. Then,
C.S.A = Curved Surface Area
Inner C.S.A of Cylinder + Outer C.S.A + Base area of top + Base area of bottom = Total C.S.A of hollow cylinder
2πrh+2πRh+2(πR2−πr2)=4620……(i)
and, Base area =πR2−πr2=115.5
π(R2−r2)=115.5
π(R+r)(R−r)=115.5……(ii)
On solving (i), we get
⇒2πh(r+R)+2(πR2−πr2)=4620
⇒2πh(r+R)+(2×115.5)=4620
⇒2π×7(r+R)+231=4620
⇒2π×7(r+R)=4620−231
⇒π(R+r)=438914=331.5……(iii)
On dividing (ii) by (iii), we get
⇒π(R+r)(R−r)π(R+r)=115.5313.5
∴R−r=719
Hence, Thickness =R−r=719=0.368 cm