Exposed surface area of joined cuboids

A small cuboid is glued onto the top of a larger cuboid. Its whole 3 cm by 2 cm base touches the larger top. Compared with adding their separate surface areas, how much area becomes internal?

If the contact length doubles while its depth stays fixed, what happens to the area removed from the sum of the two separate surface areas?

The first view shows the joined object. In the second view, the upper cuboid is lifted and transparent so you can see both touching faces. Change the contact dimensions: face A and patch B always match

What must be subtracted from the sum of the separate surface areas?

Remove both touching surfaces

First find the full surface area of each separate cuboid. Subtract the contact area twice. Then exclude any other outside face the question says is not to be covered

1. 1The contact area is C For a flat rectangular contact patch, multiply its length by its depth
2. 2An underside can still be exposed Include the lower underside unless the question explicitly excludes it
3. 3Use one length unit Convert dimensions before multiplying. The final area is in square units

Lower cuboid

\(\displaystyle S_1=152\text{ cm}^2\)

Upper cuboid

\(\displaystyle S_2=66\text{ cm}^2\)

Two cuboids have separate surface areas of 152 cm² and 66 cm². Their contact patch is 4 cm by 3 cm. Find the total outside area, including the underside

Outside area

\(\displaystyle S=194\text{ cm}^2\)

Underside dimensions

\(\displaystyle 8\text{ cm}\times6\text{ cm}\)

The same joined object has total outside area 194 cm². Its lower underside is 8 cm by 6 cm. That underside will not be painted. Find the area to paint

Lower: length, depth, height

\(\displaystyle 1.2,\ 0.8,\ 0.3\text{ m}\)

Upper: length, depth, height

\(\displaystyle 40,\ 30,\ 20\text{ cm}\)

A lower cuboid is 1.2 m by 0.8 m by 0.3 m high. An upper cuboid is 40 cm by 30 cm by 20 cm high. The whole 40 cm by 30 cm base touches the lower top. Find the outside area, including the underside

Convert the upper lengths to 0.4 m, 0.3 m and 0.2 m before finding their face areas

The separate surface areas are 152 cm² and 66 cm², with a 4 cm by 3 cm contact patch. Where is the first error in this attempt to find the total outside area?

Lower: length, depth, height

\(\displaystyle 6,\ 4,\ 2\text{ cm}\)

Upper: length, depth, height

\(\displaystyle 3,\ 2,\ 2\text{ cm}\)

A lower cuboid is 6 cm long, 4 cm deep and 2 cm high. An upper cuboid is 3 cm long, 2 cm deep and 2 cm high. Its whole 3 cm by 2 cm base touches the lower top. Find the outside area, including the underside