Question

A ball has a volume of 128 cubic inches. Find the diameter of the ball.

Answer 1

To find the diameter of the ball with a volume of 128 cubic inches, we use the formula for the volume of a sphere. By substituting the volume into the formula, solving for the radius, and multiplying the radius by 2, we find the diameter of the ball.

Step-by-step explanation:

To find the diameter of the ball, we need to use the formula for the volume of a sphere: V = (4/3)πr^3, where V is the volume and r is the radius.

Given that the volume of the ball is 128 cubic inches, we can substitute this value into the formula and solve for r.

128 = (4/3)πr^3

Dividing both sides by (4/3)π, we get:

r^3 = (128 / ((4/3)π))

Calculating r by taking the cube root of this value, we find:

r ≈ 3.109

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

Diameter = 2 × 3.109

= 6.218

Answer 2

`\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ -----\\ V=128 \end{cases}\implies 128=\cfrac{4\pi r^3}{3}\implies 128(3)=4\pi r^3`


`\bf \cfrac{128(3)}{4\pi }=r^3\implies \sqrt[3]{\cfrac{128(3)}{4\pi }}=r^3\implies \sqrt[3]{\cfrac{96}{\pi }}=r\implies \sqrt[3]{\cfrac{8\cdot 12}{\pi }}=r \\\\\\ \sqrt[3]{\cfrac{2^3\cdot 12}{\pi }}=r\implies 2\sqrt[3]{\cfrac{12}{\pi }}=r\\\\ -------------------------------\\\\ \textit{and since the diameter is \underline{twice as the radius}}\qquad d=4\sqrt[3]{\cfrac{12}{\pi }}`