The surface area of a right circular cylinder is 1200 cm^2 . If the height of the cylinder is twice its diameter, find the dimensionsof the cylinder.
I know th formula for SA is SA = 2pir^2 + 2pirh
I know h = 2d.
I know r = 1/2 d
What is h in relations to r? Is is 4r?
you are correct. h = 4r
1200 = pi r^2 h = pi * r^2 * 4r = 4pi r^3
...
I don't no
Yes, you are correct. The height (h) of the cylinder is twice its diameter (d), so h = 2d.
Since the radius (r) is half the diameter, we have r = 1/2d.
To find the dimensions of the cylinder, we need to substitute these expressions into the surface area formula:
SA = 2πr^2 + 2πrh
Substituting h = 2d and r = 1/2d:
SA = 2π(1/2d)^2 + 2π(1/2d)(2d)
Simplifying:
SA = π(1/4d^2) + πd
To solve for d, we need to set the surface area equal to 1200 cm^2:
1200 = π(1/4d^2) + πd
We can solve this equation to find the value of d, and once we have d, we can find r and h using the given relationships.
To find the dimensions of the cylinder, let's start by expressing the height (h) in terms of the radius (r).
You correctly mentioned that the height is twice the diameter (2d). Since the diameter is twice the radius (d = 2r), we can substitute d = 2r into the equation.
Therefore, h = 2d = 2(2r) = 4r.
Now that we know the relationship between h and r, we can substitute it back into the surface area formula to solve for the dimensions of the cylinder.
The surface area (SA) of a right circular cylinder is given by the formula:
SA = 2πr^2 + 2πrh.
Substituting h = 4r into the equation, we have:
SA = 2πr^2 + 2πr(4r).
Simplifying further:
SA = 2πr^2 + 8πr^2
Combining like terms:
SA = 10πr^2.
We are given that the surface area is 1200 cm^2, so we can now solve for the radius (r):
1200 = 10πr^2.
Divide both sides by 10π:
120 = r^2.
Take the square root of both sides:
√120 = r.
Simplifying further:
r ≈ 10.95 cm.
Now, to find the height (h), we can substitute the value of r back into the equation h = 4r:
h = 4(10.95)
h ≈ 43.8 cm.
Therefore, the dimensions of the cylinder are approximately r = 10.95 cm (radius) and h ≈ 43.8 cm (height).