A solid S is made up of a cylindrical part and conical part. The height of the Soild is 4.5m. The common radius of the cylindrical part and the conical part is 0.9m. The height of the conical part is 1.4m.

c. A square base pillar offside 1.6m has the same volume as soild S. Determine the height of the pillar, correct to 1 decimal place.

To determine the height of the pillar, we need to find the volume of solid S and then calculate the height of the pillar with the same volume.

Let's calculate the volume of solid S first:
The volume of the cylindrical part (V_cylinder) can be calculated using the formula V = πr^2h, where r is the radius and h is the height.
Given that the radius of the cylindrical part (r_cylinder) is 0.9m and the height (h_cylinder) of solid S is 4.5m, we can calculate the volume of the cylindrical part as follows:
V_cylinder = π * (0.9)^2 * 4.5

The volume of the conical part (V_cone) can be calculated using the formula V = 1/3 * πr^2h, where r is the radius and h is the height.
Given that the radius of the conical part (r_cone) is 0.9m and the height (h_cone) of the conical part is 1.4m, we can calculate the volume of the conical part as follows:
V_cone = 1/3 * π * (0.9)^2 * 1.4

Now, to find the total volume of solid S, we need to add the volumes of the cylindrical and conical parts:
V_solidS = V_cylinder + V_cone

Now, let's calculate the volume of the square base pillar:
The volume of a square base pillar (V_pillar) can be calculated using the formula V = l^2 * h, where l is the side length of the square base and h is the height.
Given that the side length of the pillar base is 1.6m and we want the volume to be equal to V_solidS, we can set up the equation as follows:
V_pillar = 1.6^2 * h_pillar

Since we know that V_pillar is equal to V_solidS, we can set up the equation as follows:
1.6^2 * h_pillar = V_cylinder + V_cone

Now, we have two equations:

1) V_cylinder = π * (0.9)^2 * 4.5
2) V_cone = 1/3 * π * (0.9)^2 * 1.4

Substituting these values into the equation 1.6^2 * h_pillar = V_cylinder + V_cone, we can solve for h_pillar to find the height of the pillar.

1.6^2 * h_pillar = π * (0.9)^2 * 4.5 + 1/3 * π * (0.9)^2 * 1.4

Now, calculate the right side of the equation and get the value. Finally, divide it by 1.6^2 to find the height of the pillar. Remember to round the answer to 1 decimal place.