Question

Nadia plans to paint her jewelry box. The box is shaped like a rectangular prism with the dimensions
shown. which is closest to the total surface area of the jewelry box?
​

Answer 1

Answer:

$132\ in^{2}$ is closest to the total surface area of the box

Step-by-step explanation:

we know that

The surface area of the box is equal to

$SA=2B+PH$

where

B is the area of the base

P is the perimeter of the base

H is the height of the box

we have

$L=7\frac{3}{4}\ in=\frac{7*4+3}{4}=\frac{31}{4}\ in$

$W=3\frac{1}{4}\ in=\frac{3*4+1}{4}=\frac{13}{4}\ in$

$H=3\frac{7}{8}\ in=\frac{3*8+7}{8}=\frac{31}{8}\ in$

Find the area of the base B

$B=LW$

$B=(\frac{31}{4})(\frac{13}{4})=\frac{403}{16}\ in^{2}$

Find the perimeter of the base P

$P=2(L+W)$

$P=2(\frac{31}{4}+\frac{13}{4}))$

$P=2(\frac{44}{4})=22\ in$

Find the surface area

$SA=2(\frac{403}{16})+22(\frac{31}{8})$

$SA=(\frac{403}{8})+(\frac{682}{8})$

$SA=\frac{1,085}{8}=135.625\ in^{2}$