A container with a larger surface area always has a greater volume. Explain whether or not this statement is true using several examples to support your argument.

No, this is not true every time. It depends on the conditions given.

For example-

Suppose we have a Box A with dimensions 10 x 10 x 1 and Box B with dimensions 5 x 5 x 5.

Box B has a surface area = 2 (25+25+25) = 150 and a volume of 5*5*5 = 125 cubic units

Box A has a larger surface area = 2 (100+10+10) = 240 and a smaller volume = 10*10*1 = 100 cubic units

Similarly take an example of sphere.

Lets suppose the radius of the sphere is 2 cm

So, SA is 4πr² = 4*3.14*2*2 = 50.24 cm²

Volume of the sphere is = 4πr³ / 3 = 33.50 cm³

Here also the SA is greater.