Given: Box A (cube): square base of area 36 cm² and height of 8 cm
Box B (prism): 5 × 3 × 12
Box A is completely filled with juice and Box B is empty. Then, Box A is poured into Box B until filled.
First we find the volume (V) of both boxes: V = Bh (where B is the area of the base and h is the height)
Volume of Box A = 36 × 8 = 288 [tex]cm^{3}[/tex]
Base area of Box B = 5 × 3 = 15 cm²
Volume of Box B = 15 × 12 = 180 [tex]cm^{3}[/tex]
We know that the volume of Box A is greater than the volume of Box B
(V Box A = 288, V Box B = 180)
In order to find the new volume of juice in Box A after we pour it into Box B, we subtract the volume of Box B from the volume of Box A; since Box A is poured into Box B.
288 - 180 = 108 [tex]cm^{3}[/tex]
Now that Box B is filled completely, we find the height of the new juice level in Box A
108 [tex]cm^{3}[/tex] is the amount of juice left in Box A
We know that the Base area of Box A is 36 cm²
In order to find the height of the new juice level in Box A, we use the new volume of the juice left in Box A (108 [tex]cm^{3}[/tex])
∵ V = Bh
∴ h = V ÷ B
∴ 108 ÷ 36 = 3 cm
∴ The height of the new juice level in Box A = 3 cm
