(a) The total surface area of the gold bar is 17.73 in²
(b) The volume of the gold bar is 59.04 mL
(c) The cost of the gold bar is $54,979.92
The given parameters;
length, L = 82 mm = 3.23 cm
width, W = 45 mm = 1,77 cm
depth, d = 16 mm = 0.63 cm
current price, = $1,368 per ounce
(a) The total surface area of the gold bar;
[tex]T.S.A = (2lw + 2lh + 2wh)\\\\T.S.A = 2(3.23\times 1.77) + 2(3.23 \times 0.63) + 2(1.77 \times 0.63)\\\\T.S.A = 17.73\ in^2[/tex]
(b) The volume of the gold bar
[tex]volume = lwh\\\\volume = 82 \ mm \times 45 \ mm \times 16 \ mm\\\\volume = 59,040 \ mm^3[/tex]
volume in mL = 59.04 mL
(c) The cost of the gold bar is calculated as follows;
The mass of the gold bar is calculated as;
[tex]\pi mass = density \times volume\\\\mass = 19.3 g/cm^3 \times 59.04 \ cm^3\\\\note: 1 \ mL = 1 \ cm^3\\\\mass = 1139.47 \ g\ \ = \ 40.19 \ ounce[/tex]
The cost of the gold:
[tex]cost = \frac{\$ 1,368}{ounce} \times 40.19 \ ounce = \$ 54,979.92[/tex]
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