SOLUTION: HELP HELP! A container with lid is designed in the shape of a right rectangular prism with base dimensions 11.0 cm and 14.0 cm. Determine the volume of this container if its surfa

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Question 1154326: HELP HELP!
A container with lid is designed in the shape of a right rectangular prism with base dimensions 11.0 cm and 14.0 cm. Determine the volume of this container if its surface area (including the lid) is 500.0 cm2.
Round to the nearest whole.

cm3
thank you
Found 3 solutions by mananth, MathTherapy, ikleyn:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
Surface area of rectangular prism = 2(lw+wh+lh)
Surface area = 500 cm^2 L=14, w=11 h=?
500 = ( 14*11+11h+14h)
500 = 154 +25h
500-24 =25h
476 = 25h
h= 19 cm
V= l*w*h
L=14, w=11 h=19
calculate
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
HELP HELP!
A container with lid is designed in the shape of a right rectangular prism with base dimensions 11.0 cm and 14.0 cm. Determine the volume of this container if its surface area (including the lid) is 500.0 cm2.
Round to the nearest whole.

cm3
thank you 
The other person's answer for the height is NOWHERE close to being correct. 

Correct answer: 

Now, you should be able to find the volume! 

Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
 .



We just know almost everything to calculate the volume, except the height " h " of the prism.


So, our goal is to find the height.


The surface area is 500 cm^2.

From the other side, it is  2*11*14 + 2*11*h + 2*14*h.


So, you have this equation


    2*11*14 + 2*11*h + 2*14*h = 500.


Simplify


    308 + 50h = 500

    50h = 500 - 308 = 192

      h             = 192/50 = 3.84.


Hence, the volume is  11*14*3.84 = 591.36 cm^3, or 591 cm^3  (rounded to nearest integer number, as requested).     ANSWER





Solved.





 

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