Question

Let the height of the cylinder be "h" meters, and the radius be "r" meters. Given: Volume of the cylinder = 256π cubic meters Radius (r) = 2h The formula for the volume of a cylinder is V = πr²h. Substitute the values: 256π = π(2h)²h Simplify: 256π = 4πh³ Now, divide by 4π to solve for h³: h³ = 256π / 4π h³ = 64 Now, take the cube root of both sides to find h: h = ∛64 h = 4 meters So, the height of the cylinder is 4 meters, and since the radius is twice the height, the radius is 8 meters.

Answer 1

The student is working with a cylinder volume problem. Given the Cylinder Volume = 256π cubic meters and the relation between radius and height as r = 2h, it's found that the cylinder's height is 4 meters and the radius is 8 meters.

Step-by-step explanation:

The subject of the question is in Mathematics, specifically focusing on geometry and volume calculations. The student is asked to determine the height (h) and the radius (r) of a cylinder where the volume (V) and the relationship between r and h are given. This is a common exercise in applying the formula for the volume of a cylinder (V = πr²h).

Given: Volume (V) = 256π cubic meters and radius (r) = 2h, the student can substitute these values into the volume equation: 256π = π(2h)²h. This simplifies further to 256π = 4πh³. Now, to solve for h³, the student should divide by 4π, resulting in h³ = 64. By taking the cube root of both sides, the student can find h = 4 meters. Knowing that the radius is twice the height, the student can determine that the radius is 8 meters.

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