Find the height of this cylinder given that the surface area is 628 square inches and the diameter is 10 inches.
SA = 2 π r2 + 2 π r h
628 = (2 * 3.14 * 5^2) + (2 * 3.14 * 5 * h
628 = 157 + 31.4h
471 = 31.4h
471/31.4 = h
15 = h
http://www.aaamath.com/exp79x10.htm
To find the height of the cylinder, we can use the formula for the surface area of a cylinder, which is given by:
Surface Area = 2πr² + 2πrh
where r is the radius of the base and h is the height of the cylinder.
The problem gives us the diameter of the base, which is 10 inches. We can find the radius by dividing the diameter by 2:
Radius = Diameter / 2 = 10 / 2 = 5 inches
Now we can substitute the given surface area into the formula:
628 = 2π(5)² + 2π(5)h
Simplifying further:
628 = 50π + 10πh
To isolate the height (h), we can subtract 50π from both sides:
578 = 10πh
Finally, divide both sides by 10π to solve for h:
h = 578 / (10π)
Using an approximate value of π as 3.14, we can calculate the height:
h ≈ 578 / (10 * 3.14) ≈ 18.42 inches
Therefore, the height of the cylinder is approximately 18.42 inches.