the volume, V, of a sphere in terms of its radius, r, is given by V(r) =4/3pir^3 express r as a function of v and find the radius of a sphere with volume of 400 cubic feet

Question

the volume, V, of a sphere in terms of its radius, r, is given by V(r) =4/3pir^3 express r as a function of v and find the radius of a sphere with volume of 400 cubic feet

Answer 1

Given V(r) = 4/3πr³ ,

to express r as a function of V,

we need to solve the above equation for r. (in other words, get r by itself)

V = 4/3πr³

3/4 × V = 3/4 × 4/3πr³

3/4 × V = πr³

(3/4 × V) / π = r³

the cube root of ((3/4V) / π) = r

So, r(V) = the cube root of ( (3/4V) / π ).

Next, to find the radius of a sphere with volume of 400 cubic feet,

r(400) = the cube root of ( (3/4 * 400) / π )

= the cube root of ( (300) / π )

≈ 4.57 feet [Verify with a calculator.]