Find the radius of a cone with a volume of 477mm^3 and a height of 28.5 mm.
tip: work backwards
To find the radius of the cone, we need to use the formula for the volume of a cone, which is given by:
V = (1/3)πr^2h
Where V is the volume, r is the radius, and h is the height.
In this case, we are given the volume V = 477 mm^3 and the height h = 28.5 mm. Let's substitute these values into the formula and solve for the radius r:
477 = (1/3)πr^2(28.5)
Multiply both sides of the equation by 3:
1431 = πr^2(28.5)
Divide both sides of the equation by π(28.5):
r^2 = 1431 / (π(28.5))
Simplify the right side:
r^2 = 1431 / (90π)
Take the square root of both sides of the equation:
r = √(1431 / (90π))
Using a calculator, we can approximate the value:
r ≈ 2.46 mm
Therefore, the radius of the cone is approximately 2.46 mm.
are you sure?
Apologies for the mistake in my previous response. Let's correct the calculation.
To find the radius of the cone, we can rearrange the formula for the volume of a cone and solve for the radius (r):
V = (1/3)πr^2h
Let's substitute the given values V = 477 mm^3 and h = 28.5 mm into the formula:
477 = (1/3)πr^2(28.5)
Multiply both sides of the equation by 3:
3 * 477 = πr^2(28.5)
1431 = πr^2(28.5)
Divide both sides of the equation by π(28.5):
1431 / (π(28.5)) = r^2
Divide 1431 by (π(28.5)):
r^2 = 5
Take the square root of both sides:
r = √5
Using a calculator, we can approximate the value:
r ≈ 2.24 mm
Therefore, the radius of the cone is approximately 2.24 mm.
are you really sure?
Apologies for the confusion caused. Let's recalculate the radius of the cone.
Given:
Volume of the cone (V) = 477 mm^3
Height of the cone (h) = 28.5 mm
The formula for the volume of a cone is:
V = (1/3)πr^2h
Rearranging the formula to solve for the radius (r), we have:
r = √((3V) / (πh))
Substituting the given values into the formula:
r = √((3*477) / (π*28.5))
r = √(1431 / (28.5π))
r = √(1431 / 89.54)
r ≈ √16 = 4 mm
Therefore, the radius of the cone is approximately 4 mm.