Question

question 2 an oblique cylinder with a base of radius 2 units is shown. the top of the cylinder can be obtained by translating the base by the directed line - segment ab which has length 6√2 units. the segment ab forms a 45° angle with the plane of the base. what is the volume of the cylinder? round to the nearest 10th

Explanation:

Step1: Find the height of the cylinder

Since the line - segment AB of length \(l = 6\sqrt{2}\) units makes a \(45^{\circ}\) angle with the base - plane of the cylinder, and \(\sin45^{\circ}=\frac{h}{l}\) (where \(h\) is the height of the cylinder). We know that \(\sin45^{\circ}=\frac{\sqrt{2}}{2}\) and \(l = 6\sqrt{2}\). So \(h=l\sin45^{\circ}=6\sqrt{2}\times\frac{\sqrt{2}}{2}=6\) units.

Step2: Calculate the volume of the cylinder

The formula for the volume of a cylinder is \(V=\pi r^{2}h\), where \(r = 2\) units and \(h = 6\) units. Substitute \(r = 2\) and \(h = 6\) into the formula: \(V=\pi\times2^{2}\times6=24\pi\approx24\times 3.14 = 75.4\) \(cm^{3}\).

Answer:

\(75.4\)