SAT Question 62ec6574: Area and Volume answer and explanation with Desmos solution

Choice B is correct. It's given that the base area of the right rectangular prism is $24t{\text{cm}}^2$ and the length of the base is $\frac{8}{3}$ cm. Dividing the base area by the length yields the width: $\frac{24t}{\frac{8}{3}}$, or $(24t)\left(\frac{3}{8}\right)$, or $9t$ cm. It's also given that the height of the prism is $15$ cm. A right rectangular prism has two rectangular bases and four rectangular lateral faces. The total area of the two bases is $2(24t)$, or $48t{\text{cm}}^2$. The four lateral faces include two with dimensions $\frac{8}{3}$ cm by $15$ cm and two with dimensions $9t$ cm by $15$ cm. The total area of these four lateral faces is $2\left(\frac{8}{3}\right)(15)+2(9t)(15){\text{cm}}^2$, which is equivalent to $80+270t{\text{cm}}^2$. Adding this to the total area of the two bases yields $48t+270t+80$, or $318t+80{\text{cm}}^2$. Thus, the expression, which represents the surface area, in ${\text{cm}}^2$, of the right rectangular prism is $318t+80$.