The surface area of this cylinder is 2,212.758 square millimeters. What is the height?
Use 𝜋 ≈ 3.14 and round your answer to the nearest hundredth.
r=14.5 mm
The formula for the surface area of a cylinder is given by:
Surface Area = 2𝜋r(r + h)
where r is the radius and h is the height.
We are given that the surface area is 2,212.758 square millimeters and the radius is 14.5 mm. Let's substitute these values into the formula and solve for h:
2,212.758 = 2(3.14)(14.5)(14.5 + h)
Simplifying:
2,212.758 = 6.28(14.5)(14.5 + h)
Dividing both sides by 6.28(14.5):
2,212.758/(6.28(14.5)) = 14.5 + h
Simplifying:
25.0485 = 14.5 + h
Subtracting 14.5 from both sides:
h = 25.0485 - 14.5
h ≈ 10.55
Therefore, the height of the cylinder is approximately 10.55 mm.