A circular magnet has an inner radius of x cm. An outer radius 2cm langer and its depth is the same as the inner radius If the total volume of the magnet is 120π cm3 find x?

Answer 1

The total volume of the magnetic disc (including the central hole) = π(x + 2)² x ; as x + 2 is the outer radius and x is the depth.

The volume of the inner "hole" = πx² x.

The total volume of the magnet = π(x + 2)² x - πx² x = 120π

Dividing by π gives, x³ + 4x² + 4x - x³ = 120 : x² + x = 30 : x² + x - 30 = 0

This can be factored as (x + 6)(x - 5) = 0

As we are only concerned with the positive root then this occurs when x - 5 = 0,

then x = 5

NOTE : When x² + x = 30 this could have been written as x(x + 1) = 30 and by inspection the answer 5 x 6 = 30 could be readily deduced, confirming that x = 5.