a cylinder with base area 24π cm2 and height 16 cm
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To calculate certain properties of a cylinder, we need to know its base area and height. In this case, we are given that the base area of the cylinder is 24π cm² and its height is 16 cm.
The formula for finding the volume of a cylinder is V = πr²h, where V represents volume, r represents the radius of the base, and h represents the height of the cylinder. However, in this case, we are not given the radius directly, but we can find it using the base area.
The formula for the base area of a cylinder is A = πr², where A represents the base area. By rearranging this formula, we can solve for the radius (r):
A = πr²
24π = πr²
24 = r²
To find the radius, we can take the square root of both sides:
√(24) = r
r ≈ 4.898 cm (approximated to three decimal places)
Now, we can use the obtained radius and the given height to calculate the volume. Let's substitute the values in the formula:
V = πr²h ≈ π(4.898 cm)²(16 cm) ≈ 380.132 cm³ (approximated to three decimal places)
Hence, the volume of the cylinder with a base area of 24π cm² and a height of 16 cm is approximately 380.132 cm³.