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# a cylinder has a surface area of 402 cm^2. The height is three times greater than the radius. What is the height of the cylinder?

what i did:

402 = 2πr^2+2πr(3r)

how do i separate r?

### 3 Answers by Expert Tutors

Robert B. | Experienced (10+ years), Patient, Effective.Experienced (10+ years), Patient, Effect...
4.9 4.9 (294 lesson ratings) (294)
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2π r2 + 2π r(3r) = 2π r2 + 6π r2 = 8π r2. I hope this helped, and if you need more assistance, I or another tutor will be happy to help.

Ralph L. | Algebra I, II, Visual Basic, Beginning C++ tutorAlgebra I, II, Visual Basic, Beginning C...
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2∏rh + 2∏r2 = 402

h = 4r

2∏r(4r) + 2∏r2 = 402

8∏r2 + 2∏r2 = 402

10∏r2 = 402

r2 = 402/10∏

r = √402/√10∏

h = (4√402)/√(10∏)

Nataliya D. | Patient and effective tutor for your most difficult subject.Patient and effective tutor for your mos...
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Nice start, Mathalina!!! Next, you have to simplify equation, you wrote, and solve it for "r"

2(pi)r2 + 2(pi)r(3r) = 402
2(pi)r2 + 6(pi)r2 = 402
8(pi)r2 = 402
pi = 22/7
r2 = (402/8) · (7/22)
r ≈ √15.99 = 3.0 (we use only positive value of the square root, distance cannot be negative)
h = 3r ≈ 9.0 cm