A rectangular prism has dimensions 5 by 6 by x. If the total surface area of the prism is 157.9 square units, what is the value of x?
What is the volume of the above prism?
Surface Area = 2wL +2LH + 2Hw
and you have a length of 5, a width of 6, so your height is X
157.9 = (2)(6)(5) + 2(5)(x) + 2(x)(6)
Simplify, gather like terms and solve for x
then to find the volume sub your values into Volume = LWH
thanks
You are very welcome!
To find the value of x, we need to first calculate the surface area of the rectangular prism.
The surface area of a rectangular prism can be calculated using the formula:
Surface Area = 2lw + 2lh + 2wh
Given that the dimensions are 5 by 6 by x, we can substitute the values into the formula:
157.9 = 2(5)(6) + 2(5)(x) + 2(6)(x)
Simplifying further:
157.9 = 60 + 10x + 12x
157.9 = 60 + 22x
157.9 - 60 = 22x
97.9 = 22x
To find the value of x, we divide both sides of the equation by 22:
x = 97.9 / 22
x ≈ 4.45
Therefore, the value of x is approximately 4.45.
Now let's calculate the volume of the prism.
The volume of a rectangular prism can be calculated using the formula:
Volume = length × width × height
Substituting the given values, we have:
Volume = 5 × 6 × 4.45
Volume ≈ 133.5 cubic units
Therefore, the volume of the prism is approximately 133.5 cubic units.