The figure shows a regular hexagonal prism.

The figure shows a regular hexagonal prism. The side of the hexagonal face is labeled as 4 centimeters, the length of the rectangular face is labeled as 10 centimeters, and the distance from the center of the hexagonal shape to any of its side is labeled as 3 decimal point 4 7.

Calculate the volume of the prism.
Calculate the surface area of the prism.
Round your answers to the nearest hundredth, if necessary. Show all of your work.

The figure shows a regular hexagonal prism The figure shows a regular hexagonal prism The side of the hexagonal face is labeled as 4 centimeters the length of t class=

Respuesta :

Answer:

A.415.69cm

b.323.14

Step-by-step explanation:

The height would be 10cm

The length would be 4cm

The volume of the Hexagonal prism is 415.69 centimeter cube and Surface area is 415.69 centimeter square

What is Hexagonal prism?

The hexagonal prism is a prism with hexagonal base.

What is Surface area?

The surface area of a solid object is a measure of the total area that the surface of the object occupies

What is Volume?

Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.

Given,

Base length  a= 4 centimeter

Height of the hexagonal prism h = 10 centimeter

Volume =[tex]\frac{3\sqrt{3} }{2}.a^{2}h[/tex]

Volume = [tex]\frac{3\sqrt{3} }{2}.4^{2}10[/tex] = 415.69 centimeter cube

Surface area = [tex]6ah+3\sqrt{3}.a^{2}[/tex]

Surface area = [tex]6(4)(10)+3\sqrt{3}.4^{2}[/tex] = 323.13 centimeter square

Hence, the volume of the Hexagonal prism is 415.69 centimeter cube and Surface area is 415.69 centimeter square

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