Question

Please help with the question below (please add an explanation)

Answer 1

In order to get the volume of the irregular figure, let's cut it into two regular figures. See the cut below.

First, let's calculate the volume of the upper part.

The dimensions of the upper part are 7cm by 3 cm by 3 cm. Since the shape is a rectangular prism, let's multiply 7, 3, and 3.

$V_{upper}=7cm\times3cm\times3cm=63cm^3$

Hence, the volume of the upper figure is 63 cm³.

Let's now calculate the volume of the lower figure.

The dimensions of the lower figure are 5cm by 4 cm by 3 cm. Since this is a rectangular prism too, let's multiply the dimensions.

$V_{lower}=5cm\times4cm\times3cm=60cm^3$

The volume of the lower figure is 60 cm³.

Let's add the volume of the two figures to get the volume of the entire irregular figure.

$V_{irregular}=V_{upper}+V_{lower}$$V_{irregular}=63cm^3+60cm^3=123cm^3$

Therefore, the entire volume of the given irregular figure is 123 cm³.