The difference between the outer and the inner curved surface areas of an open cylinder is $88 c m^{2}$ . If its length is $14$ cm and volume of the material in it is $176 c m^{3}$ , find the inner diameter of the cylinder.

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Solution

The correct option is A $3$ cm
Let $r_{1} =$ outer surface area, $r_{2} =$ inner surface area, length $h = 14$
Outer curved surface area of cylinder $= 2 \times π \times r_{1} \times h c m^{2}$
Inner curved surface area of cylinder $= 2 \times π \times r_{2} \times h c m^{2}$
Difference between two curved surface area cylinder $= 2 π (14) (r_{1} - r_{2}) = 88 c m^{2}$
$r_{1} - r_{2} = 1$ .......(1)
Volume of cylinder $= π (r_{1}^{2} - r_{2}^{2}) h = π (r_{1}^{2} - r_{2}^{2}) (14) = 176$
$r_{1}^{2} - r_{2}^{2} = 4$ .....(2)
Solving, (2), we get
$(r_{1} - r_{2}) (r_{1} + r_{2}) = 4$
$1 (r_{1} + r_{2}) = 4$
$r_{1} + r_{2} = 4$ .....(3)
From (1) and (3), we have
$r_{1} = \frac{5}{2}, r_{2} = \frac{3}{2}$
Inner diameter of cylinder $= 2 \times \frac{3}{2} = 3$ cm

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The difference between the outer and the inner curved surface areas of an open cylinder is 88cm2. If its length is 14 cm and volume of the material in it is 176cm3, find the inner diameter of the cylinder.

The difference between the outer and the inner curved surface areas of an open cylinder is $88 c m^{2}$ . If its length is $14$ cm and volume of the material in it is $176 c m^{3}$ , find the inner diameter of the cylinder.