Question

find the volume of the cylinder. round your answer to the nearest hundredth. 12 m 18 m 60° the volume is about □ cubic meters.

Explanation:

Step1: Find the height of the cylinder

The slant height is 18 m, and the angle is 60°. Using trigonometry, the height \( h \) of the cylinder (the adjacent side to the 60° angle) is given by \( h = 18\times\cos(60^\circ) \). Since \( \cos(60^\circ)=\frac{1}{2} \), we have \( h = 18\times\frac{1}{2}=9 \) m.

Step2: Find the radius of the cylinder

The diameter of the base is 12 m, so the radius \( r=\frac{12}{2} = 6 \) m.

Step3: Calculate the volume of the cylinder

The formula for the volume of a cylinder is \( V=\pi r^{2}h \). Substituting \( r = 6 \) m and \( h = 9 \) m, we get \( V=\pi\times6^{2}\times9 \).
First, calculate \( 6^{2}=36 \), then \( 36\times9 = 324 \). So \( V = 324\pi\approx324\times3.1415926535\approx1017.88 \) (rounded to the nearest hundredth).

Answer:

1017.88