A cylinder has surface area of 402 cm2. The height is three times greater than the radius.
What is the height of the cylinder?
r = radius
3r = height (h)
SA = 2(pi)(r)(h) + 2(pi)(r^2)
SA = 2(pi)(r)(3r) + 2(pi)(r^2)
SA = 6(pi)(r^2) + 2(pi)(r^2)
SA = 8(pi)r^2
402 = 8(pi)r^2
402 = 8(3.14)r^2
402 = 25.12r^2
16.00318 = r^2
rounding 16.00318 = 16
16 = r^2
r = 4
height = 3r = 3(4) = 12
thx
a bowling ball measures 264cm in circumference. What is the volume of the smallest cube that will hold this ball?
To solve this problem, we need to set up an equation based on the given information. Let's start by assigning variables to the unknowns.
Let's assume that the radius of the cylinder is "r." Therefore, the height of the cylinder would be "3r" since it is three times greater than the radius.
Now, let's calculate the surface area of the cylinder. The formula for the surface area of a cylinder is:
Surface Area = 2πr² + 2πrh
where π (pi) is a mathematical constant approximately equal to 3.14159.
Given that the surface area of the cylinder is 402 cm², we can substitute the variables into the formula:
402 = 2πr² + 2πrh
Now, let's simplify the equation by factoring out 2π:
402 = 2π(r² + rh)
Divide both sides of the equation by 2π:
201 = r² + rh
We can rearrange this equation in terms of height (3r) to solve for it:
201 = r² + r(3r)
201 = r² + 3r²
201 = 4r²
To isolate the square term, divide both sides of the equation by 4:
201/4 = r²
50.25 = r²
Take the square root of both sides to solve for r:
r = √50.25
Simplifying this by using a calculator, we find that the radius is approximately 7.1 cm.
Now, to find the height, which is three times the radius, we multiply the radius by 3:
Height = 3r
Height = 3(7.1)
Height = 21.3 cm
Therefore, the height of the cylinder is approximately 21.3 cm.