Question

a rectangular prism has a surface area of 310 square inches. its base is shown below. 7 in. 5 in. what is the height of the rectangular prism? inches submit

Explanation:

Step1: Recall the surface area formula

The surface area formula of a rectangular prism is \(S = 2(lw+lh + wh)\), where \(l = 7\) in, \(w = 5\) in, and \(S=310\) square inches. Let the height be \(h\).

Step2: Substitute the values into the formula

Substitute into \(S = 2(lw+lh + wh)\):

$$
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$$

Step3: Simplify the equation

Divide both sides by \(2\):

$$
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$$

Step4: Solve for \(h\)

Subtract \(35\) from both sides: \(155 - 35=12h\), so \(120 = 12h\). Then divide both sides by \(12\): \(h=\frac{120}{12}=10\)

Answer:

\(10\)