"Find the volume of a cone that has 5 as its base radius and a lateral surface area of 65 pi."
Help, thanks!
65PI=PI*5sqrt(25+h^2)
solve for height h
65/5= sqrt(25+h^2)
square both sides
169=25+h^2
h= 12
volume= 1/2 PI r^2 h
Thanks!
But that's wrong :(
The lateral area is just πrs. Don't include the area of the base.
so,
πrs = 5πs = 65π, so s = 13
So, the height is 12, making the volume
v = πr^2 h = π*25*12 = 300π
The answer is 100pi (bobpursley was right about the height but the formula he stated was incorrect)
the answer is 100pi
To find the volume of a cone, you need to know the radius of its base and its height. However, in this case, only the base radius and lateral surface area are given. So, let's start by finding the height of the cone.
The lateral surface area of a cone is given by the formula:
Lateral Surface Area = πrℓ
where r is the base radius and ℓ is the slant height of the cone.
In this case, the lateral surface area is given as 65π and the base radius is 5. We need to find the slant height, ℓ. Rearranging the formula, we get:
ℓ = Lateral Surface Area / (πr)
Substituting the given values, we have:
ℓ = 65π / (π * 5)
ℓ = 65 / 5
ℓ = 13
Now that we know the slant height (ℓ), we can calculate the height (h) of the cone using the Pythagorean theorem:
h = sqrt(ℓ^2 - r^2)
Substituting the values, we get:
h = sqrt(13^2 - 5^2)
h = sqrt(169 - 25)
h = sqrt(144)
h = 12
Now that we have the height (h) and base radius (r), we can find the volume of the cone using the formula:
Volume = (1/3) * π * r^2 * h
Substituting the values, we get:
Volume = (1/3) * π * 5^2 * 12
Volume = (1/3) * π * 25 * 12
Volume = (1/3) * π * 300
Volume = 100π
Therefore, the volume of the cone is 100π cubic units.