A birthday cake is in the shape of 2 cylinders, one smaller one on top of another larger one. The radius of the bottom layer of cake is (3x  2) and the radius of the top layer of cake is (x  4) . The height for each layer is 6 cm. Determine a simplified expression for the difference in volume between the cake layers.

6π(8x^2 + 4x - 12)

Step-by-step explanation:

Given that the radius of the bottom layer of cake is (3x + 2) and the radius of the top layer of cake is (x + 4) . The height for each layer is 6 cm

Volume of a cylinder = πr^2h

Small cylinder

Volume v = π( x + 4 )^2 × 6

v = 6π( x^2 + 8x + 16)

Big cylinder

Volume V = 6π( 3x + 2 )^2

V = 6π( 9x^2 + 12x + 4)

Expression for the difference in volume between the cake layers will be V - v

6π( 9x^2 +12x +4) - 6π( x^2 + 8x +16)

6π(8x^2 + 4x - 12)