Question

the difference between outside and inside surface of a cylinder metallic pipe 14 m long is 44 cm^2. If the sum of the diameter of the inner and outer surface is 9 cm, find the inner and outer radii of the cylinder
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Answer 1

Answer:

Outer radius = 2.5cm

Inner radius = 2cm

Step-by-step explanation:

Let, R be the external radius and r be the inner radius of the metallic pipe. h=14cm

Outer surface area−inner surface area=44cm^2

∴2πRh−2πrh=44cm^2

R-r =

$\frac{44}{2 \times \frac{22}{7} \times 14}$

$= \frac{44 \times 7}{2 \times 22 \times 14}$

R - r = 1/2

The volume of metal used =99cm^3

∴ External volume − internal volume =99cm^3

∴πR^2h - πr^2h = 99cm^3

∴πh(R^2-r^2) = 99cm^3

$\frac{22}{7} \times 14(R+ r) \times (R - r) = 99 {cm}^{3}$

$22 \times 2(R + r) \frac{1}{2} = 99 {cm}^{3}$

$R + r = \frac{99}{22} = \frac{9}{2}$

$R + r = \frac{9}{2}$

$R - r = \frac{1}{2}$

$2R = 5 \\ R = 2.5cm$

External radius = 2.5cm

$R + r = \frac{9}{2} \\ r + 2.5 = 4.5 \\ r = 4.5 - 2.5 \\ r = 2cm$

Hence, internal radius = 2cm