Find the volume of the oblique cylinder with the given radius, slant height, and angle. Note that the figure is not to scale. Enter a decimal rounded to the hundredths place.
17 cm
8 cm
50°
Find the volume of the oblique cylinder with the given radius, slant height, and angle. Note that the figure is not to scale. Enter a decimal rounded to the hundredths place. 17 cm 8 cm 50°
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To find the volume of the oblique cylinder, we use the formula for the volume of a cylinder, which is:
[ V = pi r^2 h ]
where ( r ) is the radius and ( h ) is the height. Since we have the slant height and the angle, we need to calculate the height ( h ) using the slant height and the angle.
1. Calculate the height (h):
The height can be found using the sine of the angle:
[
h = text{slant height} times sin(text{angle}) = 8 , text{cm} times sin(50^circ)
]
Using (sin(50^circ) approx 0.766):
[
h approx 8 times 0.766 approx 6.13 , text{cm}
]
2. Calculate the volume (V):
Now plug in the values:
[
r = 17 , text{cm}, quad h approx 6.13 , text{cm}
]
[
V = pi times (17^2) times 6.13 approx pi times 289 times 6.13 approx 1761.34 , text{cm}^3