Question

You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?

Answer 1

Answer:

V = 3646.5 miles^3

Step-by-step explanation:

The circumference formula applies here.  C = 2pi*r, and so r = C / [2pi].

Thus, r = 60 miles / 6.28 = 9.55 miles.

The volume formula is next.  V = (4/3)pi*r^3.

With r = 9.55 miles, this comes to     V = (4/3)(3.14)(9.55)^3 miles^3, or

V = 3646.5 miles^3

Answer 2

The volume of the sphere is about 3647.56 cubic miles.

Important information:

• Length of the great circle of a sphere = 60 miles.

Volume of sphere:

Length of the great circle of a sphere represents the circumference of the largest circle of the sphere.

$C=2\pi r$

$60=2\pi r$

$\frac{60}{2\pi}=r$

$\frac{30}{\pi}=r$

So, the radius of the sphere is $r=\frac{30}{\pi}$ miles.

Now, the volume of the sphere is:

$V=\frac{4}{3}\pi r^3$

$V=\frac{4}{3}\pi \left(\frac{30}{\pi}\right)^3$

$V=\frac{4}{3}\times \pi \times \frac{27000}{\pi^3}$

$V=\frac{36000}{\pi^2}$

$V\approx 3647.56$

Therefore, the volume of the sphere is about 3647.56 cubic miles.

Find out more about 'Volume of sphere' here:

https://brainly.com/question/381274