Question

A copper sphere of radius 5 cm is beaten and drawn into a wire of diameter 0.5 cm. Calculate the length of the wire.

• A. 26.06 m
• B. 26.60 m
• C. 26.63 m
• D. 26.66 m

Answer 1

The Correct Option is A

From the question we know that,

\(r\) = 5 cm

Volume of sphere \((V)\) = \(\frac{4}{3} \pi r^3\)

= \(\frac{4}{3} \pi (5)^3\)

= \(\frac{4}{3} \pi \times 125\)

\(\frac{500}{3} cm^3\)

=Volumn of wire \((Vw)\) = \(\pi r^2 \times length\)

\(r\ wire\) = \(\frac{0.5}{2}\) (as 0.5 is diameter)

= 0.25 cm

\(V w\) = \(\pi \times (0.25)^2 \times L\)

= \(\pi \times (0.0625) cm^2 \times L\)

= \(0.0625 \pi Lcm^3\)

\(\frac{500}{3} \pi\) = \(0.0625 \pi L\)

= \(\frac{500}{3} = 0.0625 \times L\)

\(L = \frac{500}{3 \times 0.0625}\)

\(L = \frac{500}{0.1875}\)

\(L\) ≈ 266.67 cm

\(L\) (in meter) = \(\frac{266.67}{100}\)

= 26.67 ≈ 26.66 m 

The correct option is (D): 26.66 m