Question

1. rectangular prism

a gift box measures ( 10 mathrm{~cm} \times 8 mathrm{~cm} \times 6 mathrm{~cm} ).
a. find the total surface area.
b. find the volume.

Explanation:

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

The formula for the surface area \(S\) of a rectangular prism with length \(l\), width \(w\), and height \(h\) is \(S = 2(lw+lh + wh)\).
Given \(l = 10\space cm\), \(w = 8\space cm\), \(h=6\space cm\).
Substitute the values into the formula:

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Step2: Recall the formula for the volume of a rectangular prism

The formula for the volume \(V\) of a rectangular prism is \(V=l\times w\times h\).
Substitute \(l = 10\space cm\), \(w = 8\space cm\), \(h = 6\space cm\) into the formula:

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Answer:

a. The total surface area is \(376\space cm^{2}\).
b. The volume is \(480\space cm^{3}\).