Question

1. a shipping container in the form of a cylinder has a radius of 6 feet and a length of 54 feet. what is the volume of the container, in cubic feet, rounded to the nearest tenth? 2. a sphere has a radius of 4 feet. what is the volume, in cubic feet, of the sphere rounded to the nearest hundredth?

Explanation:

Step1: Recall the formula for the volume of a cylinder

The formula for the volume of a cylinder is \(V=\pi r^{2}h\), where \(r\) is the radius and \(h\) is the height (or length in this case). Given \(r = 6\) feet and \(h=54\) feet.

Step2: Substitute the values into the formula

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Step3: Calculate the numerical value

Using \(\pi\approx3.14159\), we have \(V\approx1944\times3.14159\approx6107.3\) cubic feet.

Step4: Recall the formula for the volume of a sphere

The formula for the volume of a sphere is \(V=\frac{4}{3}\pi r^{3}\), where \(r\) is the radius. Given \(r = 4\) feet.

Step5: Substitute the values into the formula

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Step6: Calculate the numerical value

Using \(\pi\approx3.14159\), we have \(V\approx\frac{256}{3}\times3.14159\approx268.08\) cubic feet.

Answer:

1. \(6107.3\) cubic feet
2. \(268.08\) cubic feet