Answer: V ≈ 2514.9 cm3
Step-by-step explanation:
To find the volume of the prism, first calculate the area of the base.
To find the apothem of the hexagonal base, recognize that the sum of the measures of the interior angles in a hexagon is (6−2)⋅180°=720°. So, the interior angle has measure 720°6/=120°.
The base angle of the triangles with the hexagon's sides as their base is one-half of 120°, or 60°. The apothem bisects these triangles to form two right triangles with the short leg length of 5.5 cm.
By the definition of tangent, tan 60°=?/5.5.
Solve for ?.
?=5.5 ⋅ tan 60°
Therefore, the apothem length equals 5.5 ⋅ tan 60°.
The area of a hexagonal base.
B=6⋅(12⋅11⋅?)
Substitute 5.5⋅tan60° for ?.
B=6⋅(12⋅11⋅5.5 ⋅ tan60°)
Simplify.
B=181.5 ⋅ tan60° cm2
The volume of a prism.
V=Bh
Substitute 181.5 ⋅ tan60° for B and 8 for h.
V=(181.5 ⋅ tan60°)⋅8
Multiply 181.5 by 8.
V=1452 ⋅ tan60°
Use a calculator to approximate.
V≈2514.9 cm3
Therefore, the volume of the hexagonal prism is approximately 2514.9 cm3.
