A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?Choices:- 45 cm 18 cm 90 cm
Question
A metallic sphere of radius 12 cm is melted and drawn into a wire, whose radius of cross section is 16 cm. What is the length of the wire?Choices:- 45 cm 18 cm 90 cm
Solution
The volume of the sphere and the volume of the wire will be the same because the sphere is melted and drawn into the wire.
The formula for the volume of a sphere is (4/3)πr³ and the formula for the volume of a cylinder (which is the shape of the wire) is πr²h, where r is the radius and h is the height (which in this case is the length of the wire).
First, calculate the volume of the sphere: V_sphere = (4/3)π(12 cm)³ = 7238.23 cm³
Next, set this equal to the volume of the cylinder and solve for h (the length of the wire): V_sphere = V_cylinder 7238.23 cm³ = π(16 cm)²h 7238.23 cm³ = 804.25 cm³h h = 7238.23 cm³ / 804.25 cm³ = 9 cm
So, the length of the wire is 9 cm. However, none of the choices match this answer. There might be a mistake in the problem or the choices given.
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