Question

the volume, v , of a sphere in terms of its radius, r , is given by v(r)=43πr3 . express r as a function of v , and find the radius of a sphere with volume of 350 cubic feet

Answer 1

The radius r of a sphere as a function of its volume v is given by the formula r = \sqrt[3]{\frac{3v}{4\pi}}. Plugging in the volume of 350 cubic feet into this formula and evaluating it will yield the radius of the sphere.

Step-by-step explanation:

The student has provided the volume formula for a sphere, v(r) = \frac{4}{3}\pi r^3, and is asking to express the radius r as a function of volume v. To find r as a function of v, we need to rearrange the formula and solve for r.

Let's start by multiplying both sides by the reciprocal of \(\frac{4}{3}\pi\) to isolate r^3:

r^3 = \frac{3v}{4\pi}

To find the cube root, we take the cube root of both sides:

r = \sqrt[3]{\frac{3v}{4\pi}}

Now, to find the radius of a sphere with a volume of 350 cubic feet, we plug the volume into the formula:

\(r = \sqrt[3]{\frac{3\times 350}{4\pi}}\)

By calculating this expression, we can find the radius of the sphere in feet.