A right cone has a height of 8cm and of volume of 250cm^3. Determine the radius of the base of the cone to the nearest centimeter.
well, you know that
1/3 pi r^2 * 8 = 250
So, now just solve for r.
To determine the radius of the base of the cone, we can use the formula for the volume of a cone:
V = (1/3) * π * r^2 * h
Where:
V is the volume of the cone,
r is the radius of the base,
h is the height of the cone,
π is a mathematical constant approximately equal to 3.14159.
From the given information, we know that the height (h) is 8 cm and the volume (V) is 250 cm^3. We need to solve for the radius (r).
Let's substitute the given values into the formula:
250 = (1/3) * π * r^2 * 8
Next, we can simplify the equation:
250 = (8/3) * π * r^2
Now, divide both sides of the equation by (8/3) * π:
250 / ((8/3) * π) = r^2
To determine the radius (r), we need to take the square root of both sides of the equation:
r = √(250 / ((8/3) * π))
Using a calculator, we can calculate this approximately to the nearest centimeter. Using the value of π as 3.14159:
r ≈ √(250 / ((8/3) * 3.14159))
r ≈ √(250 / (2.66643 * 3.14159))
r ≈ √(250 / 8.38)
r ≈ √29.92
r ≈ 5.47
Therefore, the radius of the base of the cone, rounded to the nearest centimeter, is approximately 5 cm.