A rectangular wooden container has a base diagonal measuring 10 cm and a height of 9 cm. If its base covers an area of 48 cm², what is the total volume of the container?

The correct answer is 432 cubic cm.

To find the total volume of a rectangular wooden container, we can use the standard formula for the volume of a rectangular prism (cuboid):

$\text{Volume}=\text{Base Area}\times \text{Height}$

From the given problem, we are provided with the following parameters:
- Base Area = 48 cm²
- Height = 9 cm
- Base diagonal = 10 cm

Substituting the given values for the base area and height into the volume formula:

$\text{Volume}=48\text{cm}{2}^{}\times 9\text{cm}$

$\text{Volume}=432\text{cubic cm}$

We can also double-check the consistency of the base dimensions.
Let the length of the rectangular base be $l$ and the width be $w$.
Using the Pythagorean theorem with the base diagonal (10 cm):

$l^2+w^2={10}^2=100$

And using the given base area (48 cm²):

$l\times w=48$

Solving these simultaneous equations gives $l=8\text{cm}$ and $w=6\text{cm}$ because:
$8^2+6^2=64+36=100$
and
$8\times 6=48$

Calculating the volume using dimensions $l\times w\times h$:

$\text{Volume}=8\times 6\times 9=432\text{cubic cm}$

Thus, the total volume of the container is 432 cubic cm.