Question 140334: I can not figure this out.
A rectangular prism has a square base, a height of 10cm and a surface area of 1,050 square cm. Find its volume.
thankyou. I hope someone can help me.
Answer by jojo14344(1513)   (Show Source):
You can put this solution on YOUR website! Okay, this is a nice problem to solve.
First, Volume for rect.prism (V) = (Length)(Width)(Height)-mark this equation 1
Next, since surface area is given we need to use this since only 1 is given of the 3 unknowns in equation 1.
Surface Area = 2LH+2WH+LW (We need to add all the areas of the sides to get surface area).And now since it has square base, so the Length(L) equals the Width(W). Putting that into equation & substituting the given:
Take note that L=W
1050cm^2=2(L)(10)+2(L)(10)+2(L)(L)
1050=20L+20L+2L^2
re-arranging becomes, 2L^2+40L-1050=0
(2L-30)(L+35)=0
"L" has 2 values,
L=-35,wrong cannot be negative right?
The other value,
2L=30 ;
L=15, correct and this one to use.
Therefore, go back equation 1, V=(15)(15)(10)=2250 cu.cm. Your final answer.
To check, we need to go back to surface area given,
A=2LH+2WH+2LW, remember L=W
1050cm^2=2(15)(10)+2(15)(10)+2(15)(15)
1050cm^2=1050cm^2 smooth!
Thank you,
Jojo
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