Question

A solid sphere of diameter 6 cm is melted and then cast into cylindrical wire of radius 0.3 cm. Find the length of the wire.

• A. 50 cm
• B. 3 m
• C. 65 cm
• D. 4 m

Answer 1

Answer:

D. 4 m

The length of the wire is 400 cm (or 4 metres).

Explanation:

When an object is melted and recast into another shape, its volume remains the same.

1. Given Data:

• Sphere: Diameter = 6 cm $(\rightarrow)$Radius R = $\frac{6}{2}$ = 3 cm

• Cylindrical wire: Radius (r) = 0.3 cm

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2. Formula:

• $\text{Volume of Sphere} = \frac{4}{3}\pi R^3$

• $\text{Volume of Cylinder} = \pi r^2 h$(where h is the length of the wire)

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3. Calculation:
$\text{Volume\ of\ Cylinder}=\text{Volume\ of\ Sphere}$
$\pi r^{2}h=\frac{4}{3}\pi R^{3}$

Cancel $\pi$ from both sides:
$r^{2}h=\frac{4}{3}R^{3}$

Substitute the values:
$(0.3)^{2}\times h=\frac{4}{3}\times 3^{3}$
$0.09\times h=\frac{4}{3}\times 27$
$0.09\times h=4\times 9$
$0.09\times h=36$

Now, solve for h:
$h=\frac{36}{0.09}=\frac{3600}{9}=\mathbf{400}\text{\ }\textbf{cm}$

Converting to metres: $\frac{400}{100}$=4 metres.