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The volume of a spherical balloon is 20⅚πm³. Find the radius of the balloon.
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Sagot :

Answer:  2.5 meters

This value is exact without any rounding.

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Explanation:

The first task is to convert the mixed number 20⅚ into an improper fraction

I'll write 20⅚ as 20 & 5/6

The rule to use is a & b/c = (a*c + b)/c

So,

a & b/c = (a*c + b)/c

20 & 5/6 = (20*6+5)/6

20 & 5/6 = 125/6

This means the volume is exactly (125/6)pi cubic meters.

Plug this into the sphere volume formula and isolate the radius r like so

V = (4/3)*pi*r^3

(125/6)pi = (4/3)*pi*r^3

125/6 = (4/3)*r^3

(4/3)*r^3 = 125/6

4r^3 = 3*(125/6)

4r^3 = 125/2

r^3 = (125/2)*(1/4)

r^3 = 125/8

r = (125/8)^(1/3)

r = 5/2

r = 2.5

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