21 pointWorkbook Question \#2An 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 62 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 10 thV= type your answer... cm331 point
Q. 21 pointWorkbook Question \#2An 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 62 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 10 thV= type your answer... cm331 point
Volume Formula: The volume of a cylinder ( extit{V}) is given by the formula V=extextpir2h, where r is the radius of the base and h is the height of the cylinder.
Radius Calculation: Given that the radius r of the base is 2 units, we can square this value to find r2. So, r2=22=4 units2.
Height Determination: The height h of the cylinder is given by the length of the directed line segment AB, which is 62 units. Since the height forms a 45-degree angle with the plane of the base, and the cylinder is oblique, the actual height of the cylinder is the same as the length of AB due to the properties of a 45-degree angle in this context.
Substitution in Formula: Now we can substitute the values of r2 and h into the volume formula to calculate the volume of the cylinder: V=π×4×62.
Volume Calculation: Calculating the volume, we get V=π×4×62=π×242≈3.14159×24×1.41421≈3.14159×33.9412≈106.6 cubic units when rounded to the nearest tenth.