Question

describe and correct the error in finding the volume of the cone

13

the diameter was used instead of the radius. the volume is π cubic meters

the radius and the height should have been squared. the volume is 2π cubic meters

the units should be squared, not cubed. the volume is 4π square meters

there are two errors. the diameter was used instead of the radius, and the units should be squared, not cubed. the volume is π square meters

Explanation:

Step1: Recall the formula for the volume of a cone

The formula for the volume of a cone is \(V=\frac{1}{3}\pi r^{2}h\), where \(r\) is the radius and \(h\) is the height.

Step2: Identify the error in the given calculation

In the given calculation \(V = \frac{1}{3}(\pi)(2)^{2}(3)\), the value \(2\) is the diameter of the base of the cone. The radius \(r=\frac{d}{2}\), so \(r = 1\) m (since \(d = 2\) m).

Step3: Calculate the correct volume

Substitute \(r = 1\) m and \(h=3\) m into the formula \(V=\frac{1}{3}\pi r^{2}h\).

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Answer:

The diameter was used instead of the radius. The volume is \(\pi\) cubic meters.