A cylindrical can of volume 198cm has a height of 7cm. Find the radius of the cylinder.
as before,
v = πr^2 h
so
7πr^2 = 198
r^2 = 198/(7π)
so r = ....
To find the radius of the cylinder, we need to use the formula for the volume of a cylinder, which is given by:
Volume = π * radius^2 * height
We are given the volume (198 cm^3) and the height (7 cm). We can plug in these values into the formula and solve for the radius.
Let's rearrange the formula to solve for radius:
radius^2 = Volume / (π * height)
Now, let's substitute the given values into the formula:
radius^2 = 198 cm^3 / (π * 7 cm)
Next, simplify the expression:
radius^2 = 198 cm^3 / (22/7 * 7 cm)
radius^2 = 198 cm^3 / 22 cm
radius^2 = 9 cm^2
To solve for the radius, we take the square root of both sides:
radius = √(9 cm^2)
So, the radius of the cylinder is 3 cm.
To find the radius of the cylinder, we can use the formula for the volume of a cylinder, which is:
V = πr²h
where V is the volume, r is the radius, and h is the height.
Given that the volume of the cylindrical can is 198 cm³ and the height is 7 cm, we can plug these values into the formula:
198 = πr²(7)
To find the radius, we need to solve this equation for r.
First, divide both sides of the equation by 7:
198/7 = πr²
Simplify the left side of the equation:
28.2857 = πr²
Next, to solve for r², divide both sides of the equation by π:
28.2857/π = r²
Finally, to find r, take the square root of both sides of the equation:
√(28.2857/π) = r
Using a calculator, we get:
r ≈ 2.6807 cm
Therefore, the radius of the cylinder is approximately 2.6807 cm.