Question

find the volume of the oblique cylinder below. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Find the height of the cylinder

The slant height is 13, and the angle is 40°. Using the sine function, \( h = 13\times\sin(40^\circ) \). Calculate \( \sin(40^\circ)\approx0.6428 \), so \( h\approx13\times0.6428 = 8.3564 \).

Step2: Calculate the volume of the cylinder

The formula for the volume of a cylinder is \( V=\pi r^{2}h \), where \( r = 8 \) and \( h\approx8.3564 \). Substitute the values: \( V=\pi\times8^{2}\times8.3564=\pi\times64\times8.3564\approx64\times8.3564\times3.1416\approx64\times26.25\approx1680.0 \) (more accurately, \( 64\times8.3564 = 534.8096 \), \( 534.8096\times3.1416\approx1680.0 \)).

Answer:

The volume of the oblique cylinder is approximately \(\boxed{1680.0}\) (or more precisely, using more accurate calculations, it can be around 1680.0 when rounded to the nearest tenth).