Question

1. determine the surface area of a rectangular solid that has a height of 5 mm, a width of 7 mm, and a length of 10 mm.

Explanation:

Step1: Recall the formula for the surface area of a rectangular solid

The formula for the surface area \(S\) of a rectangular solid is \(S = 2(lw+lh + wh)\), where \(l\) is the length, \(w\) is the width, and \(h\) is the height.

Step2: Substitute the given values into the formula

Given \(l = 10\) mm, \(w = 7\) mm, \(h = 5\) mm.
First, calculate \(lw\): \(lw=10\times7 = 70\)
Then, calculate \(lh\): \(lh=10\times5=50\)
Next, calculate \(wh\): \(wh = 7\times5=35\)
Then find \(lw+lh+wh\): \(70 + 50+35=155\)
Finally, calculate \(S\): \(S = 2\times155\)

Step3: Compute the final result

\(S=310\)

Answer:

\(310\) mm²