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.

Answer: 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)