A copper rod of 1 cm diameter and 8 cm length is drawn into a wire of uniform diameter and 18 m length. The radius (in cm) of the wire, is :
A. $$\frac{1}{15}$$
B. $$\frac{1}{30}$$
C. $$\frac{2}{15}$$
D. $$15$$
Answer: Option B
Solution(By Examveda Team)
Volume of copper rod :$$\eqalign{ & = \left( {\pi \times \frac{1}{2} \times \frac{1}{2} \times 8} \right){\text{ c}}{{\text{m}}^3} \cr & = 2\pi \,{\text{ c}}{{\text{m}}^3} \cr} $$
Let the radius of the wire be r cm
Then, volume of wire :
$$\eqalign{ & = \left( \pi {r^2} \times 1800 \right) {\text{cm}}^3 \cr & = 1800\, \pi {r^2} {\text{ cm}}^3 \cr & \therefore 1800\pi {r^2} = 2\pi \cr & \Rightarrow {r^2} = \frac{2}{{1800}} \cr & \Rightarrow {r^2} = \frac{1}{{900}} \cr & \Rightarrow r = \sqrt {\frac{1}{{900}}} = \frac{1}{{30}} \cr} $$
Related Questions on Volume and Surface Area
A. 12$$\pi$$ cm3
B. 15$$\pi$$ cm3
C. 16$$\pi$$ cm3
D. 20$$\pi$$ cm3
In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
A. 75 cu. m
B. 750 cu. m
C. 7500 cu. m
D. 75000 cu. m
A. 84 meters
B. 90 meters
C. 168 meters
D. 336 meters
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