Question

a wire of radius 6 mm and length 400 m is melted into a sphere calculate the radius of the sphere in centimetres​

Answer 1

22.6 cm

Step-by-step explanation:

The volume of the wire is equal to the volume of the sphere. The volume of a cylinder (the wire) is given by the formula V = πr^2h, where r is the radius and h is the height (length). The volume of a sphere is given by the formula V = 4/3πR^3, where R is the radius of the sphere.

Let’s first convert the radius of the wire from millimeters to meters:

6 mm = 0.006 m.

The volume of the wire is then V = π(0.006 m)^2(400 m) = 0.04524 m^3.

Now we can solve for the radius R of the sphere:
0.04524 m^3 = 4/3πR^3.
Solving for R gives
R = (0.04524 m^3 / (4/3π))^(1/3) ≈ 0.226 m.

Finally, let’s convert the radius from meters to centimeters:
0.226 m = 22.6 cm.

So, the radius of the sphere is approximately 22.6 cm.