Question

question 15, 4.3.47 points: 0 of 1 use the volume of the given sphere to find the value of x. v = 2048π/3 x = (simplify your answer.)

Explanation:

Step1: Recall volume formula for sphere

The volume formula of a sphere is $V = \frac{4}{3}\pi r^{3}$.

Step2: Set up the equation

We are given $V=\frac{2048\pi}{3}$, so $\frac{4}{3}\pi r^{3}=\frac{2048\pi}{3}$.

Step3: Solve for $r$

First, cancel out $\frac{\pi}{3}$ on both sides of the equation. We get $4r^{3}=2048$. Then divide both sides by 4: $r^{3}=\frac{2048}{4}=512$. Taking the cube - root of both sides, $r = 8$. Since $x$ is the diameter of the sphere and $d = 2r$, then $x = 16$.

Answer:

$16$