Volume of the cone = 56.52 in³
Solution:
Diameter of the cone = 6 in
Radius of the cone = 6 ÷ 2 = 3 in
Height of the cone = 6 in
The value of π = 3.14
<u>To find the volume of the cone:</u>
Volume of the cone =
= 56.52
Volume of the cone = 56.52 in³
Hence the volume of the given cone is 56.52 .
Answer:
Step-by-step explanation:
To solve this problem, we will use the following two theorems/definitions:
- Given a vector field F of the form (P(x,y,z),Q(x,y,z),W(x,y,z)) then the divergence of F denoted by
- (Gauss' theorem)Given a closed surface S, the following applies
where n is the normal vector pointing outward of the surface and V is the volume bounded by the surface S.
Let us, in our case, calculate the divergence of the given field. We have that
Hence, by the Gauss theorem we have that
So, we must calculate the volume V bounded by the cube S.
We know that the vertices are located on the given points. We must determine the lenght of the side of the cube. To do so, we will take two vertices that are on the some side and whose coordinates differ in only one coordinate. Then, we will calculate the distance between the vertices and that is the lenght of the side.
Take the vertices (1,1,1) and (1,1-1). The distance between them is given by
.
Hence, the volume of V is . Then, the final answer is