Question

The volume of a sphere is 1.372 cubic inches. Find the diameter of the sphere, in inches.​

Answer 1

The formula for the volume of a sphere is given by:

V = (4/3)πr^3,

where V is the volume and r is the radius of the sphere.

To find the diameter of the sphere, we need to find the radius first. We can rearrange the formula for the volume to solve for the radius:

r = (3V / 4π)^(1/3).

Given that the volume V is 1.372 cubic inches, we can substitute this value into the formula:

r = (3 * 1.372 / (4 * π))^(1/3).

Calculating this expression gives us the radius:

r ≈ 0.589 inches.

Finally, to find the diameter, we multiply the radius by 2:

d = 2 * r = 2 * 0.589 ≈ 1.178 inches.

Therefore, the diameter of the sphere is approximately 1.178 inches.

Answer 2

To find the diameter of a sphere when given its volume, we can use the formula:

Volume = (4/3) * π * (radius)^3

In this case, the volume of the sphere is given as 1.372 cubic inches.

Let's solve the formula for the radius:

1.372 = (4/3) * π * (radius)^3

To isolate the radius, we can divide both sides of the equation by (4/3) * π:

1.372 / [(4/3) * π] = (radius)^3

Simplifying further:

1.372 * (3/4π) = (radius)^3

Now, we can take the cube root of both sides to find the radius:

radius = (1.372 * (3/4π))^(1/3)

Calculating the value:

radius ≈ 0.538 inches (rounded to three decimal places)

The diameter of the sphere is twice the radius, so:

diameter ≈ 2 * 0.538 ≈ 1.076 inches (rounded to three decimal places)

I hope this helps! :)