Question

A hollow metallic cylinder whose outer radius is 4.3cm and internal radius is 1.1m and whole length 4cm is melted and recast into a solid cylinder 12cm long. Find the diameter of the solid cylinder

Answer 1

R=4.3cm
r=1.1cm
h=4cm
therefore volume=π(R²-r²)h
π(R-r)(R+r)h
π(4.3-1.1)(4.3+1.1)×4
π(3.2)(5.4)×4
69.12π cm³
when melted
h=12cm
r=?
therefore πr²h=69.12π
r²×12=6912/100
r²=6912/100×12
r²=576/100
r=√576/√100
r=24/10
r=2.4cm

diameter=2r
d=2×2.4
d=4.8cm

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Answer 2

The diameter of the solid cylinder is 4.8 cm.

• The inner radius of cylinder is given as 1.1cm and the outer radius is 4.3cm.

• The length of the cylinder is 4 cm.

• Volume of the cylinder is π × ($r_1^2 - r_2^2$) × h.

Volume of the cylinder = π × [(4.3)² - (1.1)²] × 4 = 69.12π cm³.

• Now the given cylinder is melted and recast into a solid cylinder of height 12cm , we have to find the diameter of the cylinder so formed.

• Volume of the above cylinder is equal to the volume of the solid cylinder.

69.12π = πr²H

69.12 = r² (12)

r² = 5.76

r = 2.4 cm.

• Radius of the solid cylinder is 2.4 cm.

• Now diameter of the circle is 2r = 2× 2.4 = 4.8 cm.