A cylinder has a surface area of 339 square centimeters and a radius of 6 centimeters. Estimate the volume of the cylinder to the nearest whole number
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I don't get it!
To estimate the volume of the cylinder, we first need to find the height (or length) of the cylinder.
The surface area of a cylinder is given by the formula:
Surface Area = 2πr(r + h)
In this case, we are given the surface area (339 square centimeters) and the radius (6 centimeters).
339 = 2π(6 + h)
To solve for h, divide both sides of the equation by 2π:
339 / (2π) = 6 + h
To isolate h, subtract 6 from both sides of the equation:
(339 / (2π)) - 6 = h
Now we can calculate the value of h using a calculator:
h ≈ (339 / (2π)) - 6
Next, we can use the formula for the volume of a cylinder to estimate the volume. The formula is:
Volume = πr^2h
Using the given radius (6 centimeters) and the calculated height (h), we can estimate the volume:
Volume ≈ π(6)^2h
Evaluate the expression using the approximate value of h obtained from the previous step, and calculate the result:
Volume ≈ π(6)^2 * h
Finally, round the estimated volume to the nearest whole number.
A=2πrh+2πr^2
339 = (2 * 3.14 * 6 * h) + (2 * 3.14 * 6^2)
Can you take it from there?