Find the volume of a regular hexagonal prism if the measure of one side of the base is 14 and the height is 10.
a.)140√2 cm^3
b.)2940√3 cm^3
c.)140 cm^3
I was thinkin the answer is 140√2 cm^3
V=NAh=6(14x12.1/2)10=5082cubic cm
V=volume; N=number of sides=number of triangles that forms base of hexagon;
A=area of each triangle(quanity in parenthesis); h=height of hexagon.
The 6 triangles formed by drawing a line from the center to each vertex are equalateral. Therefore, the height of each triangle is 14sin60=12.1. I hope this explanation is sufficient.
To find the volume of a regular hexagonal prism, you need to know the length of one side of the base (which is given as 14) and the height (which is given as 10).
The formula for the volume of a prism is V = base area x height.
For a regular hexagon, the area of the base can be found using the formula: A = (3√3/2) x s^2, where s is the length of one side of the hexagon.
Let's first find the area of the base:
A = (3√3/2) x s^2
A = (3√3/2) x 14^2
A = (3√3/2) x 196
A = (3 x 3.464/2) x 196
A = 10.392 x 196
A = 2,037.552 cm^2
Now, we can calculate the volume:
V = base area x height
V = 2,037.552 cm^2 x 10 cm
V = 20,375.52 cm^3
So, the correct answer is b.) 20,375.52 cm^3, not a.) 140√2 cm^3.