3) surface area of the box = 162 in²
4) surface area of the box = 16200 in²
6) Volume of the box = 0.104 in³
Explanation:
The dimensions of the box:
length = 8in
width = 6 1/2 in = 6.5 in
Height = 2 in
3) surface area of the box = surface area of a rectangular prism
surface area of a rectangular prism = 2(lh + wh + lw)
surface area of a rectangular prism = 2(8 ×2 + 6.5 × 2 + 8 × 6.5)
= 2(16 + 13 + 52)
surface area of a rectangular prism = 2(81) = 162
surface area of the box = 162 in²
4) If the dimensions are scaled up by a factor of 10:
we will multiply each of the initial dimensions by 10. Then we will find the new surface area
length = 8(10) = 80 in
width = 6.5(10) = 65 in
height = 2(10) = 20 in
surface area of the box = 2(lh + wh + lw) = 2lh + 2wh + 2lw
surface area of the box = 2(80)(20) + 2(65)(20) + 2(80)(65)
= 3200 + 2600 + 10400
surface area of the box = 16200 in²
6) Volume of a rectangular prism = l × w × h
initial dimensions: l = 8 in, w = 6.5 in , h = 2 in
Volume of a rectangular prism = volume of the box
Volume of the box = 8 × 6.5 × 2
Volume of the box = 104 in³
The volume we got is the initial/old volume
[tex]\frac{new\text{ volume }}{\text{old volume }}=(scalefactor)^3[/tex][tex]\begin{gathered} \text{scale factor = 1/10} \\ \frac{new\text{ volume}}{104}\text{ = (}\frac{1}{10})^3 \\ \text{new volume = 104 }\times\frac{1^3}{10^3}\text{ = 104 }\times\frac{1}{1000} \\ \text{new volume = }\frac{104}{1000}=0.104in^3 \end{gathered}[/tex]
Hence, the volume of the box if it scaled down by a factor of 1/10 is 0.104 in³
