SOLUTION: The total surface area of a right square prism is 230 ft^2. Find the height of the prism if the length of a side of a base is 5 ft.
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-> SOLUTION: The total surface area of a right square prism is 230 ft^2. Find the height of the prism if the length of a side of a base is 5 ft.
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Question 1076963: The total surface area of a right square prism is 230 ft^2. Find the height of the prism if the length of a side of a base is 5 ft. Found 2 solutions by ankor@dixie-net.com, ikleyn:Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! The total surface area of a right square prism is 230 ft^2.
Find the height of the prism if the length of a side of a base is 5 ft.
:
let h = the height
We know it has a square base
L = 5' is the length of the base
w = 5' is the width of the base
:
surface area
SA = 2(Lw) + 2(Lh) + 2(wh)
2(5*5) + 2(5h) + 2(5h) = 230
simplify, divide by 2
25 + 5h + 5h = 115
10h = 115 - 25
10h = 90
h = 90/10
h = 9' is the height
;
;
Check:
2(5*5) + 2(5*9) + 2(5*9) =
50 + 90 + 90 = 230
The base area is 5*5 = 25 ft^2.
Then 230-2*25 = 180 ft^2 is the lateral surface area.
Then 180/4 = 45 ft^2 is the area of a single lateral face.
Then = 9 ft is the height.
