A cylinder has a height that is 2 times as large as its radius. The lateral area of the
cylinder is 16 square units. What is the length of the radius of the cylinder?
i think it’s 2 units
Unfortunately, your answer is incorrect. Here's how to solve the problem:
Let's call the radius of the cylinder "r" and the height "h". We know that h = 2r, since the height is twice as large as the radius.
We also know that the lateral area of the cylinder is 16 square units. The lateral area is the area of the curved surface of the cylinder, which is given by the formula 2πrh. Substituting h = 2r and the given lateral area of 16, we get:
2πr(2r) = 16
4πr^2 = 16
r^2 = 4
r = 2
Therefore, the length of the radius of the cylinder is 2 units, which is the correct answer.
i said it was 2 units
I apologize – you are correct, you did say the answer was 2 units. I misread your response. Good job, you got the correct answer!
To find the length of the radius of the cylinder, we can follow these steps:
1. Begin by understanding the given information. The problem states that the height of the cylinder is 2 times as large as its radius. Let's denote the radius as 'r'. Therefore, the height is 2r.
2. The formula for the lateral area of a cylinder is given by the equation: Lateral Area = 2πrh, where π is a constant and r is the radius of the cylinder.
3. Substitute the given values into the formula. The problem states that the lateral area of the cylinder is 16 square units. So we have: 16 = 2πrh.
4. Now, substitute the height and the radius in terms of 'r' into the equation. The height is given as 2r, so we have: 16 = 2πr * 2r.
5. Simplify the equation: 16 = 4πr^2.
6. Divide both sides of the equation by 4π to solve for r^2: r^2 = 16 / (4π).
7. Simplify further: r^2 = 4 / π.
8. Take the square root of both sides to find the value of 'r': r = √(4 / π).
9. Approximate the value using a calculator or consider π to be 3.14: r ≈ √(4 / 3.14).
10. Calculating the approximate value of 'r': r ≈ √1.27389.
11. The approximate value of 'r' is approximately 1.128.
Therefore, the length of the radius of the cylinder is approximately 1.128 units.