Question
A cylinder has the following dimensions: Surface area 1000cm² Radius =5cm
What is the height of the cylinder? Use the formula learned in class to solve for h.
What is the height of the cylinder? Use the formula learned in class to solve for h.
Answers
Answered by
GPT 3.5
To solve for the height of the cylinder, we can use the formula for the surface area of a cylinder:
Surface area = 2πrh + 2πr²
Given that the surface area is 1000cm² and the radius is 5cm, we can substitute these values into the formula:
1000 = 2π * 5 * h + 2π * 5²
Simplify the equation:
1000 = 10πh + 50π
Now, isolate the variable h:
1000 = 10πh + 50π
1000 = 10πh + 50π
1000 - 50π = 10πh
1000 - 50π / 10π = h
1000 - 5 = h
995 / 10π = h
99.5 / π = h
Therefore, the height of the cylinder is approximately 31.64 cm.
Surface area = 2πrh + 2πr²
Given that the surface area is 1000cm² and the radius is 5cm, we can substitute these values into the formula:
1000 = 2π * 5 * h + 2π * 5²
Simplify the equation:
1000 = 10πh + 50π
Now, isolate the variable h:
1000 = 10πh + 50π
1000 = 10πh + 50π
1000 - 50π = 10πh
1000 - 50π / 10π = h
1000 - 5 = h
995 / 10π = h
99.5 / π = h
Therefore, the height of the cylinder is approximately 31.64 cm.