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21 point
Workbook 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 
6sqrt2 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 th

V=" type your answer... "cm^(3)
3
1 point

2121 point\newlineWorkbook Question \#22\newlineAn oblique cylinder with a base of radius 22 units is shown. The top of the cylinder can be obtained by translating the base by the directed line segment AB A B which has length 62 6 \sqrt{2} units. The segment AB A B forms a 45 45^{\circ} angle with the plane of the base. What is the volume of the cylinder? Round to the nearest 1010 th\newlineV= type your answer... cm3 V=\text { type your answer... } \mathrm{cm}^{3} \newline33\newline11 point

Full solution

Q. 2121 point\newlineWorkbook Question \#22\newlineAn oblique cylinder with a base of radius 22 units is shown. The top of the cylinder can be obtained by translating the base by the directed line segment AB A B which has length 62 6 \sqrt{2} units. The segment AB A B forms a 45 45^{\circ} angle with the plane of the base. What is the volume of the cylinder? Round to the nearest 1010 th\newlineV= type your answer... cm3 V=\text { type your answer... } \mathrm{cm}^{3} \newline33\newline11 point
  1. Volume Formula: The volume of a cylinder ( extit{V}) is given by the formula V=extextpir2hV = ext{ extpi}r^2h, where rr is the radius of the base and hh is the height of the cylinder.
  2. Radius Calculation: Given that the radius rr of the base is 22 units, we can square this value to find r2r^2. So, r2=22=4r^2 = 2^2 = 4 units2^2.
  3. Height Determination: The height hh of the cylinder is given by the length of the directed line segment ABAB, which is 626\sqrt{2} units. Since the height forms a 4545-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 ABAB due to the properties of a 4545-degree angle in this context.
  4. Substitution in Formula: Now we can substitute the values of r2r^2 and hh into the volume formula to calculate the volume of the cylinder: V=π×4×62V = \pi \times 4 \times 6\sqrt{2}.
  5. Volume Calculation: Calculating the volume, we get V=π×4×62=π×2423.14159×24×1.414213.14159×33.9412106.6V = \pi \times 4 \times 6\sqrt{2} = \pi \times 24\sqrt{2} \approx 3.14159 \times 24 \times 1.41421 \approx 3.14159 \times 33.9412 \approx 106.6 cubic units when rounded to the nearest tenth.

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