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The total surface area is made up of three pairs of sides for a total of six sides.

We must find
Area_{hw}, which is the area of the side that is h by
w.

Area_{hw}
= (h)(w)

We must find
Area_{hl}, which is the area of the side that is h by
l.

Area_{hl}
= (h)(l)

We must find
Area_{wl}, which is the area of the side that is w by
l.

Area_{wl}
= (w)(l)

Each of the above areas are present on two sides of the box. So, the total surface area is sum of twice each of these areas, that is:

Total
Surface Area = 2(Area_{hw}) + 2(Area_{hl})
+ 2(Area_{wl})

The volume of the box is simply the product of h, w, and l.

Volume = (h)(w)(l)

Example:

Let h = 3 cm, w = 5 cm, l = 8 cm

Area_{hw} =
(h)(w) = (3 cm)(5 cm) = 15 cm^{2}

Area_{hl} =
(h)(l) = (3 cm)(8 cm) = 24 cm^{2}

Area_{wl} =
(w)(l) = (5 cm)(8 cm) = 40 cm^{2}

Total Surface Area =
2(Area_{hw}) + 2(Area_{hl}) + 2(Area_{wl})

Total Surface Area =
2(15 cm^{2}) + 2(24 cm^{2}) + 2(40 cm^{2})

Total Surface Area = 30
cm^{2} + 48 cm^{2} + 80 cm^{2}

Total Surface Area =
158 cm^{2}

Volume = (h)(w)(l)

Volume = (3 cm)(5 cm)(8 cm)

Volume = 120 cm^{3}

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