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

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Mathematics

Luca Benton

7 January, 09:14

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

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Salma Chaney · 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)

Step-by-step 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)