Answer
a. $A=2s^2+4hs$
b. $h=\frac{A-2s^2}{4s}$ and 14cm
c. $A=6s^2$
Work Step by Step
Part a: Surface area formula for rectangular prism is $A=2(wl+hl+hw)$
Next, substitute formula with given height, length, and width: $A=(s(s)+h(s)+h(s))$
Simplify: $A=2(s^2+hs+hs)$. Then combine like terms: $A=2(s^2+2hs)$
Lastly distribute: $A=2s^2+4hs$
Part b: Using the answer to part a, isolate h. Start by subtracting 2s^2 from both sides of the equation to get $A-2s^2=4hs$. Next, divide 4s from both sides of the equation to get $\frac{A-2s^2}{4s}=h$. Using this new formula, substitute the given values for A and s. $\frac{760-2(10^2)}{4(10)}=h$. $h=14$
Part c: Using the formula for the surface area of a rectangular prism $A=(s(s)+h(s)+h(s))$, substitute h, l, and w with s since they are equivalent to each other. $A=2(s(s)+s(s)+s(s))$ Next, simplify: $A=2(s^2+s^2+s^2)$. Combine like terms: $A=2(3s^2)$ Lastly, distribute: $A=6s^2$
