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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.

Respuesta :

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.
Lanuel

The volume of the cylinder to the nearest whole number is 23,867 cubic meters.

Given the following data:

  • Surface area of cylinder = 1850 square meters
  • Radius of cylinder = 9 meters.

To calculate the volume of the cylinder to the nearest whole number:

How to calculate surface area.

Mathematically, the surface area (SA) of a cylinder is given by this formula:

[tex]SA = 2\pi rh + 2\pi r^2[/tex]

Where:

  • h is the height.
  • r is the radius.

Making h the subject of formula, we have:

[tex]h= \frac{SA-2\pi r^2 }{2\pi r} [/tex]

Substituting the given parameters into the formula, we have;

[tex]h= \frac{1850-(2\times 9^2) }{2\times 9} \\\\h= \frac{1850-(2\times 81) }{18} [/tex]

Height, h = 93.78 meters.

Now, we can calculate the volume of the cylinder:

[tex]Volume = base\;area \times height\\ \\ Volume = 3.142 \times 9^2 \times 93.78[/tex]

Volume = 23,866.632 ≈ 23,867 cubic meters.

Read more on surface area here: https://brainly.com/question/21367171

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