SOLUTION: Would someone please help? The surface area, A, of a cylinder in terms of its radius, r, and height, h, is given by A = 2πr^2 + 2πrh. If the height of the cylinder is 4

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: Would someone please help? The surface area, A, of a cylinder in terms of its radius, r, and height, h, is given by A = 2πr^2 + 2πrh. If the height of the cylinder is 4       Log On

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Question 1137748: Would someone please help?
The surface area, A, of a cylinder in terms of its radius, r, and height, h, is given by
A = 2πr^2 + 2πrh.
If the height of the cylinder is 4 feet, express the radius as a function of A.
r(A) =
Find the radius if the surface area is 350 square feet. (Round your answer to two decimal places.)
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
(Some help only)

A = 2πr^2 + 2πrh
2pi%2Ar%5E2%2B2pi%2Arh-A=0

h=4given:

2pi%2Ar%5E2%2B8pi%2Ar-A=0
r=%28-8pi%2B-+sqrt%2864pi%5E2%2B4%2A2%2AA%29%29%2F4
r=%28-8pi%2B-+2%2Asqrt%2864pi%5E2%2B2A%29%2F4
r=%28-4pi%2B-+sqrt%2864pi%5E2%2B2A%29%29%2F2
but not yet finished.
Needed restrictions are 64pi%5E2%2B2A%3E=0, and sqrt%2864pi%5E2%2B2A%29%3E4pi
.
.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

The surface area, A, of a cylinder in terms of its radius,+r, and height, h, is given by
A+=+2pi%2Ar%5E2+%2B+2pi%2Ar%2Ah
If the height of the cylinder is h=4feet, express the radius as a function of A.
A+=+2%2Api%2Ar%5E2+%2B+2%2Api%2Ar%2A4 .....solve for r
A+=+2%2Api%2Ar%5E2+%2B+8%2Api%2Ar
A+=+2%2Api%28r%5E2+%2B+4r%29
r%5E2+%2B+4r=A+%2F2pi ...........complete the square on left side
%28r%5E2+%2B+4r%2Bb%5E2%29-b%5E2=A+%2F2pi ....b=2
%28r%5E2+%2B+4r%2B2%5E2%29-2%5E2=A+%2F2pi
%28r%2B2%29%5E2-4=A+%2F2pi
%28r%2B2%29%5E2=A+%2F2pi%2B4
r%2B2=sqrt%28A+%2F2pi%2B4%29
r%28A%29+=sqrt%28A+%2F2pi%2B4%29-2

Find the radius if the surface area is 350 square feet. (Round your answer to two decimal places.)
r%28A%29+=sqrt%28350+%2F2pi%2B4%29-2
r%28A%29+=sqrt%2859.73248407643312%29-2
r%28A%29+=7.728679322913658-2
r%28A%29+=5.73 feet