A cylinder has a surface area of 1850 square meters and a radius of 9 meters. Estimate the volume of the cylinder to the nearest whole number. The volume is about \( \square \) cubic meters.

To estimate the volume of the cylinder, we can use the formula for the volume \( V \) of a cylinder, which is \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height. First, we need to find the height. The surface area \( A \) of a cylinder is given by \( A = 2\pi r(h + r) \). Plugging in the values we know: 1850 = 2π(9)(h + 9). Solving for \( h \): 1850 = 18π(h + 9). Now, divide both sides by \( 18\pi \): \( h + 9 = \frac{1850}{18\pi} \). To find \( h \): \( h = \frac{1850}{18\pi} - 9 \). Now, we'll substitute \( r \) and \( h \) back into the volume formula to find \( V \). After calculating, we find the height, then use it to compute: \( V = \pi (9^2) h \). Ultimately, the volume is about \( 1,217 \) cubic meters when rounded to the nearest whole number!