Question

5 cm
Solid A
2 cm
3 cm
4 cm
Solid B
12 cm
4 cm
The surface areas of the two solids shown above are equal.

Answer 1

The LHS and RHS are not equal.

If we were to flip the solid on the left so its parallel to the solid on the right, we would be able to compare the two more easier.

We can see that the right solid has dimensions of:

L = 5 cm

W = 2 cm

H = 3 cm

The left solid has dimensions of:

L = 4

W = 12

H = 4

If we were to add these all up, they would not equal.

R: 4 + 12 + 4 = 20

L: 5 + 2 + 3 = 10

The total surface area of a solid is the sum of the areas of all of the faces or surfaces that enclose the solid. The faces include the tops and bottoms (bases) and the remaining surfaces. The lateral surface area of a solid is the surface area of the solid without the bases.

The surface area of any solid shape is the sum of the areas of all faces in that solid shape.

For example, when finding the surface area of a cuboid we add the area of each rectangle constituting the cuboid.

There are three types of surface area: lateral surface area , curved surface area, and total surface area.

• The total surface area of a combined solid is the sum of the total surface areas of the individual solids that make up the combined solid, excluding the overlapping parts from each figure.

• Whereas the volume of a combined solid is the sum of the volumes of the individual solids that make up the combined solid.

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