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)
