Question

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.

Answer 1

To estimate the volume of the cylinder with a surface area of 1850 square meters and a radius of 9 meters, we need to calculate the height of the cylinder using the formula for surface area and rearranging it to solve for height. Then, we can calculate the volume using the formula for the volume of a cylinder. The estimated volume of the cylinder is approximately 3466 cubic meters.

Step-by-step explanation:

To estimate the volume of the cylinder, we first need to calculate the radius and height of the cylinder using the given information. The radius is given as 9 meters. To find the height, we can rearrange the formula for surface area of a cylinder:

A = 2πrh + πr²

Simplifying the formula to solve for h:

h = (A - πr²) / (2πr)

Plugging in the values for A = 1850 square meters and r = 9 meters:

h = (1850 - (3.142 × 9²)) / (2 × 3.142 × 9) ≈ 41.15 meters

Now that we have the radius (9 meters) and height (41.15 meters), we can calculate the volume using the formula:

V = πr²h

Plugging in the values:

V ≈ 3.142 × (9²) × 41.15 ≈ 3466 cubic meters

Therefore, the estimated volume of the cylinder is 3466 cubic meters.

Answer 2

area of a cylinder is the area of the top + the area of the bottom + the area of the wrap-around (lateral)
top: pi*r*r=81pi
bottom: 81pi
lateral: 2pi*r*h=18pi*h, h is unknown, but you don't have to solve it.

add them up: 81pi +81pi + 18h*pi=1850
pi*h=(1850-162pi)/18, (plug this in the volume formula below.)

volume of a cylinder: the area of the base × the height =81pi*h
volume=81[1850-162pi)/18]
use your calculator: V=6036

please double check my calculation by yourself.