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
To find the inner radius (r) of the can, we need to use the formula for the volume of a cylinder, which is given by:
V = πr²h
where V represents the volume, r represents the radius, and h represents the height of the cylinder.
From the information given in the question, we know that the height (h) of the can is 20 centimeters and the capacity (V) is 2600 cm³.
So, we can rewrite the formula as:
2600 = πr²(20)
To find the value of r, we need to solve this equation.
Divide both sides of the equation by 20π:
2600 / (20π) = r²
130 / π = r²
Now, take the square root of both sides of the equation to solve for r:
√(130 / π) = r
Using a calculator, we can approximate the value of π to 3.14.
√(130 / 3.14) ≈ 6.01
Therefore, the inner radius (r) of the can is approximately 6.01 cm (rounded to one decimal place).