Page 299 - Start Up Mathematics_8 (Non CCE)

Example 41: The difference between the outside and inside surface of a cylindrical iron pipe 21 cm long is
2
3
66 cm . If the pipe is made of 99 cm of metal, find the outer and inner radii of the pipe.
Solution: Let the external radius of the pipe be R cm and the internal radius be r cm.
Length of the pipe (h) = 21 cm

Now, Outside area – Inside area = 66 cm 2
fi 2pRh – 2prh = 66
fi 2ph(R – r) = 66
22
fi 2 × × 21 × (R – r) = 66
7

fi (R – r) = 66 ¥ 7 = 1 ...(1)
2 ¥ 22 ¥ 21 2
Volume of metal used = 99 cm 3
fi External volume – Internal volume = 99 cm 3
2
2
fi pR h – pr h = 99
2
2
fi ph(R – r ) = 99
fi ph(R + r) (R – r) = 99
22 1
fi × 21 × × (R + r) = 99 {Substituting the value of R – r from (1)}
7 2
fi 33 × (R + r) = 99
99
fi R + r = = 3 ...(2)
33
Solving (1) and (2), we get

7
R = cm = 1.75 cm, r = 1.25 cm
4
\ Outer radius of pipe = 1.75 cm and inner radius of pipe = 1.25 cm
Example 42: The cost of painting the total outside surface of a closed cylindrical oil tank at 70 paise per
square dm is ` 770. The height of the tank is 6 times the radius of the base of the tank. Find
the volume of the oil tank.
Solution: Let the radius of the base be r dm and the height of the cylinder be h dm, then h = 6r
Total surface area = 2pr(h + r) = 2pr(6r + r) = 2pr(7r) = 14pr 2
70 49
2
Cost of painting = ` (14pr ) × = ` pr 2
100 5
But the cost of painting is ` 770.
49
2
fi pr = 770
5
49 22
2
fi × × r = 770
5 7
2
fi r = 770 57¥¥ = 25
49 22¥
2
fi r = 25 fi r = 5 dm
\ h = 6 × 5 = 30 dm
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