Question

4.9 surface area and volume of composite
surface area =
pi = 3.14 round answer to 2 decimal places
mm²

Explanation:

Step1: Calculate surface - area of bottom cuboid

The surface - area formula for a cuboid is $2(lw + lh+wh)$. For the bottom cuboid with $l = 15$ mm, $w = 9$ mm, $h = 5$ mm, its surface - area $S_1=2(15\times9 + 15\times5+9\times5)=2(135 + 75 + 45)=2\times255 = 510$ $mm^2$. But we need to subtract the area of the contact part with the top cuboid. The contact part has an area of $6\times6$ $mm^2$. So the adjusted surface - area of the bottom cuboid $S_{1a}=510- 6\times6=510 - 36=474$ $mm^2$.

Step2: Calculate surface - area of top cuboid

For the top cuboid with side length $a = 6$ mm, its total surface - area is $6a^2=6\times6\times6 = 216$ $mm^2$. But we need to subtract the area of the contact part with the bottom cuboid (which is $6\times6$ $mm^2$). So the adjusted surface - area of the top cuboid $S_{2a}=216-6\times6=216 - 36 = 180$ $mm^2$.

Step3: Calculate total surface - area of composite shape

The total surface - area $S=S_{1a}+S_{2a}=474 + 180=654$ $mm^2$.

Answer:

$654.00$ $mm^2$