Question

The difference between the outer and inner curved surface areas of a hollow right circular cylinder, 14 cm long, is 88 cm2. If the volume of metal used in making the cylinder is 176 cm3, find the outer and inner diameters of the cylinder. (Use $\pi = \frac{22}{7} )$ (AI 2010)

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Answer 1

Answer:let r be inner radius and R be outer radius

¤=pi

Then,2¤Rh-2¤rh=88

2¤h(R-r)=88

¤(R-r)=88/2*14

¤(R-r)=88/28

¤(R-r)=22/7

22/7(R-r)=22/7

(R-r)=22*7/7*22

(R-r)=1 ....... (i)

Volume =¤R^2h - ¤r^2h=176

¤h(R2-r2)=176

22*14/7(R2-r2)=176

44(R2-r2)=176

(R2-r2)=176/44

(R+r)(R-r)=4

(R+r)*1=4

(R+r)=4 ...... (ii)

By solving (i) and (ii),

2R=5

R=2.5 cm

Outer diameter=2*2.5=5 cm

R+r=4

2.5+r=4

r=1.5 cm

Inner diameter=1.5*2=3 cm

Step-by-step explanation:

Answer 2

Answer:

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