Question

A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high. (i) Which box has the greater lateral surface area and by how much? (ii) Which box has the smaller total surface area and by how much?​

Answer 1

has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high. (i) Which box has the greater lateral surface area and by how much? (ii) Which box has the smaller total surface area and by how much

Answer 2

Answer:

The cube with an edge length of 10cm has a greater lateral surface area of 400$cm^{2}$. The cuboid only has an area of 360$cm^{2}$

The cuboid however has a greater total surface area with 610$cm^{2}$ while the cube only has 600$cm^{2}$.

Step-by-step explanation:

The lateral surface area of any 3-D shape is the area of the walls excluding the top and the bottom.

For a cube, that would be 4$a^{2}$ because $a^{2}$ is the area of any one surface area of the cube.

For a cuboid, that would be 2(lxh)+2(bxh). (Draw a cuboid shape on a piece of paper to understand this better).

By this formula, the cube's LSA comes out to be $4(10)^{2}$. This equals to 4(100) and thus 400$cm^{2}$.

Cuboid's LSA comes out to be 2(12.5x8)+2(10x8). This equals 2(100)+2(80)=200+160=360$cm^{2}$.

The total surface area of any 3-D shape is area of all walls including the top and the bottom.

For a cube, this would be 6$a^{2}$. Thus, 6(100) which is 600$cm^{2}$.

For a cuboid, that would be 2[(lxb)+(bxh)+(hxl)]. This gives us 2(100+80+125)=610$cm^{2}$