Given:
- Slant height of the frustum of the cone = 5 cm
- Difference between the radii of the circular ends = 4 cm

To find:
- Height of the frustum of the cone

Solution:
Let's assume that the radii of the larger and smaller circular ends of the frustum are R cm and r cm, respectively.

Step 1: Identify the key formulas:
- Slant height of the frustum of the cone = Difference in the radii of the circular ends / Height of the frustum
- Slant height of the frustum of the cone = √((R - r)^2 + h^2)
- Height of the frustum of the cone = sqrt((R - r)^2 + h^2)

Step 2: Substitute the given values into the formula:
- R - r = 4 cm (Given)
- Slant height = 5 cm (Given)

Step 3: Solve the equation to find the height:
- √((R - r)^2 + h^2) = 5 cm (Equation 1)
- (R - r)^2 + h^2 = 25 cm^2 (Square both sides of Equation 1)
- (R - r)^2 = 25 - h^2 (Rearrange the equation)
- R^2 - 2Rr + r^2 = 25 - h^2 (Expand the squared term)
- R^2 - 2Rr + r^2 - 25 + h^2 = 0 (Rearrange the equation)

Step 4: Substitute the given value of R - r into the equation:
- (4)^2 - 2(4)(r) + r^2 - 25 + h^2 = 0
- 16 - 8r + r^2 - 25 + h^2 = 0
- r^2 - 8r + h^2 - 9 = 0 (Equation 2)

Step 5: Find the values of r and h using the quadratic formula:
- r = [8 ± sqrt((-8)^2 - 4(1)(h^2 - 9))] / 2
- r = [8 ± sqrt(64 - 4h^2 + 36)] / 2
- r = [8 ± sqrt(100 - 4h^2)] / 2
- r = [8 ± 2sqrt(25 - h^2)] / 2
- r = 4 ± sqrt(25 - h^2)

Step 6: Determine the height of the frustum by substituting the value of r:
- Height of the frustum = sqrt((R - r)^2 + h^2)
- Height of the frustum = sqrt((4 - (4 ± sqrt(25 - h^2)))^2 + h^2)

Step 7: Simplify the equation and solve for h:
- Squaring both sides of the equation gives:
- (4 - (4 ± sqrt(25 - h^2)))^2 + h^2 = h^2
- (