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

Answer: (A)

26.06 m

Answer 2

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