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# A rectangular prism is painted mauve

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A rectangular prism 3cm by 5cm by 8cm is painted mauve and is then cut into 1 cm cubes what is the total unpainted surface area of these cubes

Oct 29, 2020

#1
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118 painted sides

720 Total sides

720 - 118 = 602 Unpainted sides

Oct 29, 2020
#2
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A rectangular prism 3cm by 5cm by 8cm is painted mauve and is then cut into 1 cm cubes. what is the total unpainted surface area of these cubes ?

Hello Guest!

$$n=\frac{V}{1\cdot cm^3}=\frac{3\cdot 5\cdot 8\cdot cm^3}{1\cdot cm^3}=\color{blue}120$$

$$S_{unpainted}=n\cdot 6\cdot cm^2=120\cdot 6\cdot cm^2=\color{blue}720cm^2$$

$$S_{inside}=S_{unpainted}-S_{outside}=720cm^2-2\cdot (3\cdot 5+3\cdot 8+5\cdot 8)cm^2$$

$$S_{inside}=562cm^2$$

!

Oct 29, 2020