A cone has a height of 10cm and a volume of 9cm cubed. what is the radius of the cone?
If the radius is r
Vol = (1/3) π r^2 h
9 = (1/3)*π*r^2*10
27 = 10π r^2
r^2 = 27/(10π) = ....
take √ to get r
My answer was 2.5570=2.56
To find the radius of a cone given its height and volume, you need to use the formula for the volume of a cone. The formula for the volume of a cone is:
V = (1/3) * π * r² * h
Where:
V = Volume of the cone
π ≈ 3.14159 (pi)
r = Radius of the base of the cone
h = Height of the cone
In this case, you are given the height of the cone, which is 10 cm, and the volume of the cone, which is 9 cm³. You need to rearrange the formula to solve for the radius (r).
Let's substitute the given values into the formula and solve for the radius:
9 = (1/3) * π * r² * 10
First, divide both sides of the equation by 10:
9/10 = (1/3) * π * r²
Next, multiply both sides of the equation by 3 to eliminate the fraction:
(9/10) * 3 = π * r²
27/10 = π * r²
Now, divide both sides of the equation by π:
(27/10) / π = r²
To isolate r², divide both sides of the equation by 27/10:
r² = (27/10) / π
Finally, take the square root of both sides to solve for the radius, r:
r = √[(27/10) / π]
Using a calculator, you can find the approximate value of the radius.