Cylindrical Height and Diameter

[Guest]

8000 1/4 in. buckshot are melted and formed into a cylinder. The height and diameter are equal. Determine diameter and height.

5% allowance is made for waste in melting.

The buckshot are spheres.

Sphere volume = 4pi (r^3 /3).

Cylinder volume = pi * r^2 * height.

Unsure how to solve.

[Guest]

Please reply. Thanks.

[Guest]

As you say, the volume of a sphere of radius r is given by $\frac{4}{3}\pi r^3$ while a cylinder with radius r and height also r has volume $\pi r^3$. Use the first formula to calculate the volume of a "1/4 inch buckshot" (is that 1/4 inch radius or diameter). Multiply by 8000 to determine the volume of 8000 buckshot. Take the cube root of that divided by $\pi$.

[Guest]

4/3 * pi * r^3

1.333 * 3.1416 * .125 * .125 * .125 = .00817 cu. in. (volume for 1).

.00817 * 8000 = 65.36 cu. in.

cube root: 4.0281

4.0281 / 3.1416 = 1.282

Are my calculations correct ?