Question

A cylinder has a circular base with a radius r. The height of the cylinder is half of r.Use the fact that the volume of a cylinder with a circular base is 휋푟:ℎ.a.Find a function that models the surface area Softhe cylinder in terms of r. Use correct function notation.b.Find a function that models the volume Vofthe cylinderin terms of r only.Use correct function notation.c.Find a function that models the surface area Sof the cylinderin terms of its volume V. Use correct function notatio

Answer 1

S(r) = 3*π*r^(2)

V(r) = π*r^(3)/2

S(v) = 3*π* (cubic roof (2*V(r)/π)^(2)

Explanation:

S(r) = lateral area + (area of base + area of top)

S(r) = 2*π*r*h + 2*π*r^(2) S(r) =2*π*r*r/2 + 2*π*r^(2) = π*r^(2) + 2π*r^(2)

S(r) =3*π*r^(2)

V(r) =π*r^(2)*h since h=r/2 V(r) =π*r^(3)/2

r^(3) = 2*V(r)/π r = cubic roof (2*V(r)/π)

And S(v) = 3*π* (cubic roof (2*V(r)/π)^(2)