A cylinder has a surface area of 2,512 square feet. The height
of the cylinder is three times the radius of the base of the cylinder
Find the radius and the height of the cylinder
type the solution
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A cylinder has a surface area of 2,512 square feet. The height
of the cylinder is three times the radius of the base of the cylinder
Find the radius and the height of the cylinder
type the solution
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Answer:
Let's denote the radius of the base of the cylinder as "r" and the height of the cylinder as "h."
From the information given, we have two pieces of information:
1. The surface area of the cylinder is 2,512 square feet, which can be calculated using the formula for the lateral surface area of a cylinder:
Lateral Surface Area = 2 * π * r * h = 2,512 square feet
2. The height of the cylinder is three times the radius:
h = 3r
Now, we can set up a system of equations based on these two pieces of information:
Equation 1: 2 * π * r * h = 2,512
Equation 2: h = 3r
First, we can substitute the value of h from Equation 2 into Equation 1:
2 * π * r * (3r) = 2,512
Now, let's solve for r:
6πr^2 = 2,512
Divide both sides by 6π:
r^2 = 2,512 / (6π)
r^2 ≈ 133.23
Now, take the square root of both sides to find the radius:
r ≈ √(133.23)
r ≈ 11.55 feet (rounded to two decimal places)
Now that we have the radius, we can find the height using Equation 2:
h = 3r
h = 3 * 11.55
h ≈ 34.65 feet (rounded to two decimal places)
So, the radius of the cylinder is approximately 11.55 feet, and the height is approximately 34.65 feet.