A rectangular prism has dimensions 4 by 6 by x. If the total surface area of the prism is 496 square units, what is the value of x?
To find the value of x, we need to use the formula for the total surface area of a rectangular prism.
The total surface area of a rectangular prism can be calculated using the formula:
Surface Area = 2lw + 2lh + 2wh
Given that the dimensions are 4 by 6 by x, we can substitute these values into the formula:
496 = 2(4)(6) + 2(4)(x) + 2(6)(x)
Now we can simplify the equation:
496 = 48 + 8x + 12x
Next, we combine like terms:
496 = 48 + 20x
Now, we can solve for x by isolating the variable:
496 - 48 = 20x
448 = 20x
Dividing both sides by 20:
448/20 = x
Simplifying:
22.4 = x
Therefore, the value of x is 22.4.
To find the value of x, we need to use the formula for the total surface area of a rectangular prism. The formula is:
Surface Area = 2lw + 2lh + 2wh
Given that the dimensions of the rectangular prism are 4 by 6 by x, we can substitute these values in the formula:
496 = 2(4)(6) + 2(4)(x) + 2(6)(x)
Now, we can simplify the equation:
496 = 48 + 8x + 12x
Combine like terms:
496 = 48 + 20x
Subtract 48 from both sides:
496 - 48 = 20x
448 = 20x
Divide both sides by 20:
448/20 = x
The value of x is 22.4.
Therefore, the value of x in the rectangular prism is 22.4.
just add up all the faces and solve for x:
2(4*6 + (4+6)x) = 496
48+20x = 496
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