A briefcase in the shape of a rectangular prism has a height of 10 cm and a volume of 4,875 cm³. What is the area of the base of the briefcase?

A. 243.75 cm²
B. 487.5 cm²
C. 2,437.5 cm²
D. 4,865 cm²



Answer :

To solve for the area of the base of the briefcase, we need to use the information given about its volume and height. The briefcase is described as a rectangular prism, and for such a shape, the formula for volume [tex]\( V \)[/tex] is given by:

[tex]\[ V = \text{Base Area} \times \text{Height} \][/tex]

Here, we know:
- The volume [tex]\( V \)[/tex] is [tex]\( 4875 \, \text{cm}^3 \)[/tex]
- The height [tex]\( h \)[/tex] is [tex]\( 10 \, \text{cm} \)[/tex]

We need to find the base area [tex]\( A \)[/tex]. To do so, we rearrange the formula to solve for the base area:

[tex]\[ A = \frac{V}{h} \][/tex]

Substituting the given values into this formula:

[tex]\[ A = \frac{4875 \, \text{cm}^3}{10 \, \text{cm}} \][/tex]

[tex]\[ A = 487.5 \, \text{cm}^2 \][/tex]

Therefore, the area of the base of the briefcase is [tex]\( 487.5 \, \text{cm}^2 \)[/tex].

So, the correct choice is:
[tex]\[ \boxed{487.5 \, \text{cm}^2} \][/tex]