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# Find the ratio between the total surface area of a cylinder

Question:

Find the ratio between the total surface area of a cylinder to its curved surface area, given that height and radius of the tank are 7.5 m and 3.5 m respectively.

Solution:

Given that,

Radius of the cylinder (r) = 3.5 m

Height of the cylinder (h) = 7.5 m

Total Surface Area of cylinder (T. S. A)

= 2πr(r + h)

Curved surface area of a cylinder (C.S.A)

= 2πrh

Now,

$\frac{\text { T.S. A }}{\text { C.S. A }}=\frac{2 \pi r(r+h)}{2 \pi r h}$

$=\frac{h+r}{h}$

Putting the values in eq (1)

$=\frac{7.5+3.5}{7.5}$

$=11 / 7.5$

$=\frac{11 * 10}{7.5}$

= 22/15

= 22:15

Therefore the ratio is 22:15.