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The volume of a sphere is 523.33 ft cubed. To the nearest foot​, what is the radius of the​ sphere? Use 3.14 for pi.

Feb 10, 2020

#1
+1

The volume of a sphere is 523.33 ft cubed. To the nearest foot​, what is the radius of the​ sphere? Use 3.14 for pi.

The formula is                              V = (4/3) π r3

Plug in known values                    523.33  =  (4/3) • 3.14 • r3

Do a little arithmetic                      523.33  =  4.187 • r3

Divide both sides by 4.187            128.047  =  r3

We know that 5 cubed is 125, so the cube root of 128.047 will be slightly larger than 5.

To get the exact cube root,

I'll have to use a calculator ..... and the answer is ..... r = 5.04  see below

When I put 5.04 back into the formula, the answer came out high.  This would be the effect of rounding that I did along the way.  When I work it on the calculator with no rounding, then r3 = 124.999.... that's close enough to 125 to say the radius is 5, therefore r = 5.

.

Feb 10, 2020
edited by Guest  Feb 10, 2020

#1
+1

The volume of a sphere is 523.33 ft cubed. To the nearest foot​, what is the radius of the​ sphere? Use 3.14 for pi.

The formula is                              V = (4/3) π r3

Plug in known values                    523.33  =  (4/3) • 3.14 • r3

Do a little arithmetic                      523.33  =  4.187 • r3

Divide both sides by 4.187            128.047  =  r3

We know that 5 cubed is 125, so the cube root of 128.047 will be slightly larger than 5.

To get the exact cube root,

I'll have to use a calculator ..... and the answer is ..... r = 5.04  see below

When I put 5.04 back into the formula, the answer came out high.  This would be the effect of rounding that I did along the way.  When I work it on the calculator with no rounding, then r3 = 124.999.... that's close enough to 125 to say the radius is 5, therefore r = 5.

.

Guest Feb 10, 2020
edited by Guest  Feb 10, 2020