two similar containers have base areas 26cm² and 324cm² respectively. Calculate the capacity of the larger container correct to one decimal place if the capacity of the smaller one is 8cm²

The Correct Answer Is 351.9 cm^3

351.9 cm³

Step-by-step explanation:

The ratio of the areas of two similar solids is equal to the square of the ratio of the lengths.

A₂ / A₁ = (s₂ / s₁) ²

The ratio of the volumes of two similar solids is equal to the cube of the ratio of the lengths.

V₂ / V₁ = (s₂ / s₁) ³

Therefore, we can say:

V₂ / V₁ = (A₂ / A₁) ^ (3/2)

Plugging in values:

V / 8 cm³ = (324 cm² / 26 cm²) ^ (3/2)

V = 351.9 cm³