There are two similar prisms Prism 1 has a surface area of 2

There are two similar prisms. Prism 1 has a surface area of 289 ft^2 and Prism 2 has a surface area of 529 ft^2. If Prism 2 has a volume of 24334 ft^3, what is the volume of Prism 1?

Solution

Given that SA of Prism1 = 289 ft² and SA of Prism 2 = 529 ft². Volume of Prism 2 = 24334 ft³.

Therefore the scaling factor = Sqrt(289)/Sqrt(529) = 17/23

Now when we have to find the volume, the ratio should be cubed = 17³/23³ = 4913/12167

Now this Ratio is equal to the ratio of actual volumes.

Let the volume of Prism 1 be x ft³. Therefore x/24334 = 4913/12167. Solving x = (24334*4913)/12167

Therefore x, the volume of Prism 1 = 9826 ft³.