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Question
A hollow metallic cylindrical tube has an internal radius of 3.5 cm and height 21 cm. The thickness of the metal tube is 0.5 cm. The tube is melted and cast into a right circular cone of height 7 cm. Find the radius of the cone, correct to one decimal place.
Solution
lnternal radius of the hollow cylinder = r = 3.5 cm
Height = h = 21 cm
Thickness of the metal = 0.5 cm
Therefore, Outer radius= R = (3.5+0.5) cm = 4 cm
Now, Volume of metal used = `pih(R^2 - r^2)`
= `22/7 xx 21 xx (4^2 - 3.5^2)`
= `22/7 xx 21 xx (16 - 12.25)`
= `22/7 xx 21 xx 3.75`
= 247.5 cm3
Volume of metal used = 247.5 cm3
Therefore, Volume of cone= 247.5 cm3 and height = 7 cm
Let r1 be the radius of cone.
∴ Volume = `1/3pir1^2h`
⇒ `1/3 pir1^2h = 247.5`
⇒ `1/3 xx 22/7 xx r1^2 xx 7 = 247.5`
⇒ `r1^2 = (247.5 xx 3 xx 7)/(22 xx 7)`
⇒ `r1^2 = 33.75`
⇒ `r1 = 5.8 "cm"`
Radius of the cone = 5.8 cm
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