Question

Two containers are mathematically similar.
The surface area of the larger container is 226 cm2

and the surface area of the smaller container is 94 cm2
.

The volume of the larger container is 680 cm3
.
Find the volume of the smaller container.

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

Since the two containers are mathematically similar, their corresponding dimensions are proportional. Let's denote the ratio of the dimensions of the smaller container to those of the larger container by k. Then, we have:

Surface area of smaller container = k^2 × surface area of larger container

Volume of smaller container = k^3 × volume of larger container

We are given that the surface area of the larger container is 226 cm^2 and the surface area of the smaller container is 94 cm^2. So, we can write:

k^2 × 226 = 94

Solving for k, we get:

k = sqrt(94/226) ≈ 0.559

Now, we can use this value of k to find the volume of the smaller container:

Volume of smaller container = k^3 × volume of larger container

Volume of smaller container = (0.559)^3 × 680

Volume of smaller container ≈ 135.7 cm^3

Therefore, the volume of the smaller container is approximately 135.7 cm^3