Consider the solid S described below.
A right circular cone with height 7h and base radius 2r
Find the volume V of this solid
It's calculus and it's in my homework.
To find the volume of the solid S, which is a right circular cone, we can use the formula for the volume of a cone.
The formula for the volume of a cone is V = (1/3) * π * r^2 * h, where r is the radius of the base of the cone and h is the height of the cone.
In this case, the height of the cone is given as 7h and the radius of the base is given as 2r.
Substituting these values into the formula, we have:
V = (1/3) * π * (2r)^2 * (7h)
Simplifying, we get:
V = (1/3) * π * 4r^2 * 7h
Multiplying the constants, we have:
V = (4/3) * π * r^2 * 7h
Or, simplifying further, we get:
V = (28/3) * π * r^2 * h
Therefore, the volume V of the solid S is (28/3) * π * r^2 * h.
To find the volume of the solid S, we need to use the formula for the volume of a cone, which is given by:
V = (1/3) * π * r^2 * h,
where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the base radius of the cone, and h is the height of the cone.
In the problem given, the height is 7h and the base radius is 2r. To find the volume, substitute these values into the volume formula:
V = (1/3) * π * (2r)^2 * (7h).
Simplifying the expression:
V = (1/3) * π * 4r^2 * 7h.
V = (4/3) * π * r^2 * 7h.
V = (28/3) * π * r^2 * h.
So, the volume of the solid S is (28/3) * π * r^2 * h.
Use the standard formula for a cone.
V = (1/3) pi*r^2*h
It makes no sense to call the height 7h and the radius 2r, unless you are comparing two different cones.
h and r are the height and radius, respectively
This is not calculus