If the surface area of a cylinder is 288π cm2 with radius of 8 cm, what is the volume of the cylinder?

The volume of the cylinder is 640π cm³

Step-by-step explanation:

The formula of the surface area of a cylinder is SA = 2πrh + 2πr², where r is the radius of its base and h is its height

The formula of the volume of a cylinder is V = πr²h

Let us use the formula of the surface area to find the height of the cylinder, then use the formula of the volume to find its volume

∵ The surface area of a cylinder is 288π cm²

∵ Its radius is 8 cm

∵ SA = 2πrh + 2πr²

- Substitute the SA by 288π and r by 8 in the formula

∴ 288π = 2π(8)h + 2π(8)²

∴ 288π = 16πh + 128π

- Subtract 128π from both sides

∴ 160π = 16πh

- Divide both sides by 16π

∴ 10 = h

∴ The height of the cylinder is 10 cm

Now let us find the volume of the cylinder

∵ V = πr²h

- Substitute r by 8 and h by 10

∴ V = π(8)²(10)

∴ V = π(64)(10)

∴ V = 640π

The volume of the cylinder is 640π cm³

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to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.