Question

A certain hexagonal prism has a volume of 160 cubic meters. Its base has a perimeter of 30 meters and an area of 64 square meters. What is the surface area in square meters of the hexagonal prism??

Answer 1

Answer:

The surface area is equal to $203\ m^{2}$

Step-by-step explanation:

step 1

Find the height of the prism

we know that

The volume of the prism is equal to

$V=Bh$

where

B is the area of the base of the prism

h is the height of the prism

we have

$V=160\ m^{3}$

$B=64\ m^{2}$

substitute in the formula and solve for h

$160=64h$

$h=160/64=2.5\ m$

step 2

Find the surface area

The surface area of the prism is equal to

$SA=2B+Ph$

where

B is the area of the base of the prism

P is the perimeter of the base

h is the height of the prism

we have

$B=64\ m^{2}$

$P=30\ m$

$h=2.5\ m$

substitute in the formula

$SA=2(64)+(30)(2.5)=203\ m^{2}$