Sure, let's solve this step by step.

Step 1: Find the volume of the copper wire.
The volume (V) of a cylinder (which is the shape of the wire) can be found using the formula V = πr²h, where r is the radius and h is the height (or length in this case). The radius is half the diameter, so r = 1.5 cm / 2 = 0.75 cm. The length of the wire is 80 m, but we need to convert this to cm because the radius is in cm. So, h = 80 m * 100 = 8000 cm.

So, V = π * (0.75 cm)² * 8000 cm = 14137166.94 cubic cm.

Step 2: Find the radius of the spherical ball.
The volume of a sphere can be found using the formula V = 4/3 * π * r³. We know the volume from step 1, so we can set this equal to the volume of the sphere and solve for r.

14137166.94 cubic cm = 4/3 * π * r³

Solving for r, we get r = cube root of (14137166.94 * 3/4π) = 15.02 cm.

So, the radius R of the spherical ball is approximately 15.02 cm.

Question

Sure, let's solve this step by step.

Step 1: Find the volume of the copper wire.
The volume (V) of a cylinder (which is the shape of the wire) can be found using the formula V = πr²h, where r is the radius and h is the height (or length in this case). The radius is half the diameter, so r = 1.5 cm / 2 = 0.75 cm. The length of the wire is 80 m, but we need to convert this to cm because the radius is in cm. So, h = 80 m * 100 = 8000 cm.

So, V = π * (0.75 cm)² * 8000 cm = 14137166.94 cubic cm.

Step 2: Find the radius of the spherical ball.
The volume of a sphere can be found using the formula V = 4/3 * π * r³. We know the volume from step 1, so we can set this equal to the volume of the sphere and solve for r.

14137166.94 cubic cm = 4/3 * π * r³

Solving for r, we get r = cube root of (14137166.94 * 3/4π) = 15.02 cm.

So, the radius R of the spherical ball is approximately 15.02 cm.

Knowee AI · Accepted Answer

Sure, let's solve this step by step.

Step 1: Find the volume of the copper wire.
The volume (V) of a cylinder (which is the shape of the wire) can be found using the formula V = πr²h, where r is the radius and h is the height (or length in this case). The radius is half the diameter, so r = 1.5 cm / 2 = 0.75 cm. The length of the wire is 80 m, but we need to convert this to cm because the radius is in cm. So, h = 80 m * 100 = 8000 cm.

So, V = π * (0.75 cm)² * 8000 cm = 14137166.94 cubic cm.

Step 2: Find the radius of the spherical ball.
The volume of a sphere can be found using the formula V = 4/3 * π * r³. We know the volume from step 1, so we can set this equal to the volume of the sphere and solve for r.

14137166.94 cubic cm = 4/3 * π * r³

Solving for r, we get r = cube root of (14137166.94 * 3/4π) = 15.02 cm.

So, the radius R of the spherical ball is approximately 15.02 cm.

If a copper wire of diameter 1.5 cm and length 80 m is melted completely and recast to form a solid spherical ball of radius R cm, then find the value of R (in cm).

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