What is the surface area of a right rectangular prism where each edge length measures 15.10 cm? (1 point) 8,208.36cm^2 1,350cm^2 900cm^2 1,368.06cm^2

1 answer

To determine the surface area of a right rectangular prism (also known as a rectangular box), we can use the formula for the surface area \( S \) of a rectangular prism:

\[ S = 2(lw + lh + wh) \]

where \( l \), \( w \), and \( h \) are the lengths of the three edges of the prism.

In this case, since all edges are equal (the prism is a cube), we have:

\[ l = w = h = 15.10 , \text{cm} \]

Plugging in the values:

\[ S = 2(l^2 + l^2 + l^2) = 2(3l^2) = 6l^2 \]

Now, substituting \( l = 15.10 , \text{cm} \):

\[ S = 6(15.10^2) \]

Calculating \( 15.10^2 \):

\[ 15.10^2 = 228.01 , \text{cm}^2 \]

Now, substitute this value into the surface area formula:

\[ S = 6(228.01) = 1368.06 , \text{cm}^2 \]

Thus, the surface area of the right rectangular prism is:

\[ \boxed{1,368.06 , \text{cm}^2} \]

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