Question

question 2 of 5. a company makes different sized shoeboxes in the shape of rectangular prisms. match the area of the material needed to make each box to the boxs dimensions. drag the tiles to the correct boxes to complete the pairs. 10 in × 6 in × 6 in, 312 in², 16 in × 6 in × 4 in, 368 in², 324 in², 330 in², 12 in × 5 in × 6 in, 14 in × 5 in × 5 in

Explanation:

Step1: Recall surface - area formula for rectangular prism

The surface - area formula of a rectangular prism with length $l$, width $w$, and height $h$ is $SA = 2(lw+lh + wh)$.

Step2: Calculate surface area for $10$ in $\times6$ in $\times6$ in box

$SA_1=2(10\times6 + 10\times6+6\times6)=2(60 + 60+36)=2\times156 = 312$ in$^2$.

Step3: Calculate surface area for $16$ in $\times6$ in $\times4$ in box

$SA_2=2(16\times6+16\times4 + 6\times4)=2(96+64 + 24)=2\times184=368$ in$^2$.

Step4: Calculate surface area for $12$ in $\times5$ in $\times6$ in box

$SA_3=2(12\times5+12\times6 + 5\times6)=2(60+72 + 30)=2\times162 = 324$ in$^2$.

Step5: Calculate surface area for $14$ in $\times5$ in $\times5$ in box

$SA_4=2(14\times5+14\times5+5\times5)=2(70 + 70+25)=2\times165=330$ in$^2$.

Answer:

$10$ in $\times6$ in $\times6$ in box - $312$ in$^2$
$16$ in $\times6$ in $\times4$ in box - $368$ in$^2$
$12$ in $\times5$ in $\times6$ in box - $324$ in$^2$
$14$ in $\times5$ in $\times5$ in box - $330$ in$^2$