Final answer:
The volume of a cylinder with a base area of 36 Pi inches squared and a height equal to the radius is 216 Pi cubic inches or approximately 678.6 cubic inches when rounded to the nearest tenth.
Step-by-step explanation:
To find the volume of a cylinder with a base area of 36 Pi inches squared and a height equal to the radius, we use the formula for the volume of a cylinder V = πr²h. Given that the base area A is 36π, we first find the radius r by the formula for the area of a circle A = πr², which gives us r² = 36, so r = 6 inches. Since the height h is equal to the radius, h = 6 inches as well.
Plugging these values into the formula for cylinder volume gives us:
V = πr²h = π(6 inches)²(6 inches) = 216π cubic inches.
To express it without Pi and rounded to the nearest tenth:
V = 216π ≈ 216 x 3.14159 ≈ 678.6 cubic inches (rounded to the nearest tenth).
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