Two containers have base areas of 750 cm2
and 120cm 2
respectively. Calculate the volume of the larger
container given that the volume of the smaller containers is 400cm2.
the problem leaves out the fact that the two figures are similar. In that case, we can find the larger volume using
the fact that the volumes grow as the 3/2 power of the base areas.
x/400 = (750/120)^(3/2)
x = 6250
Apologies for the oversight. Given that the two containers are similar, we can use the fact that the volumes of similar objects grow as the 3/2 power of their corresponding lengths or areas.
In this case, the volume of the larger container (x) is related to the volume of the smaller container (400 cm^2) by their corresponding base areas:
x / 400 = (750 cm^2 / 120 cm^2)^(3/2)
Simplifying the equation:
x / 400 = (6.25)^(3/2)
Calculating (6.25)^(3/2):
x / 400 = 15.625
Multiplying both sides of the equation by 400:
x = 6250 cm^3
Therefore, the volume of the larger container is 6250 cm^3.
To find the volume of a container with a given base area, we can multiply the base area by the height.
Let's assume the bigger container has a height of h.
The volume of the smaller container is 400 cm^2. We can find the height of the smaller container by dividing the volume by its base area:
Height of smaller container = Volume of smaller container / Base area of smaller container
Height of smaller container = 400 cm^2 / 120 cm^2
Height of smaller container = 3.33 cm (rounded to two decimal places)
Now, we can use the height of the smaller container to find the volume of the bigger container using the same formula:
Volume of bigger container = Base area of bigger container * Height of bigger container
Volume of bigger container = 750 cm^2 * h
Since the volume of the bigger container is not given, we cannot solve for h.