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.
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