A manufacturer of tin cans wishes to construct a right circular cylindrical can of height 20 centimeters and capacity 2600 cm^3 (see the figure). Find the inner radius r of the can. (Round your answer to one decimal place.)
r = cm
V=πr^2h
2600 = 3.14 * r^2 * 20
2600 = 62.8 * r^2
2600 / 62.8 = r^2
41.40127 = r^2
6.4 = r
To find the inner radius of the can, we can use the formula for the volume of a right circular cylinder, which is given by:
V = π * r^2 * h
where V is the volume, r is the radius, and h is the height.
In this case, we know that the height of the can is 20 centimeters and the capacity (volume) is 2600 cm^3. We can substitute these known values into the formula:
2600 = π * r^2 * 20
To solve for the inner radius, we can rearrange the equation and isolate r by dividing both sides of the equation by (π * 20):
2600 / (π * 20) = r^2
Simplifying the equation:
2600 / (20 * π) = r^2
To find r, we can take the square root of both sides of the equation:
r = sqrt(2600 / (20 * π))
Using a calculator, we can calculate the value of r:
r ≈ 4.08 cm
Therefore, the inner radius of the can is approximately 4.08 cm.