Two containers have base areas of 750 cm2

Question

and 120cm 2
respectively. Calculate the volume of the larger
container given that the volume of the smaller containers is 400cm2.

Answer 1

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.

Answer 2

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

Answer 3

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.