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.

a. Calculate the volume,correct to 1 decimal place,of soild S.

b. Calculate the total surface area of soild S.

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.

If I know how to do it. I will not post

sigh.

(a) v = π * 0.9^2 * 3.1 + 1/3 * π * 0.9^2 * 1.4
(b) a = π * 0.9^2 + 2π * 0.9 * 3.1 + π * 0.9 * √(0.9^2 + 1.4^2)
(c) 1.6^2 * h = (volume from (a))

Just use your basic formulas for volume and area ...

To find the volume of the solid S, we need to calculate the volumes of the cylindrical part and the conical part separately, and then add them together.

a. Volume of the cylindrical part:
The volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.
Given the radius of the cylindrical part is 0.9m and the height of the solid is 4.5m, we can calculate the volume of the cylindrical part as follows:
V_cylinder = π(0.9)^2(4.5)
V_cylinder ≈ 11.39 cubic meters (rounded to 1 decimal place)

b. Volume of the conical part:
The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
Given the radius of the conical part is 0.9m and the height 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)
V_cone ≈ 0.79 cubic meters (rounded to 1 decimal place)

c. Total volume of the solid S:
To find the total volume of solid S, we add the volume of the cylindrical part and the volume of the conical part:
V_total = V_cylinder + V_cone
V_total ≈ 11.39 + 0.79
V_total ≈ 12.18 cubic meters (rounded to 1 decimal place)

Now let's calculate the total surface area of solid S.

c. Total surface area of the solid S:
To find the total surface area, we need to calculate the surface area of each part separately and then add them together.

Surface area of the cylindrical part:
The surface area of a cylinder can be calculated using the formula A = 2πrh + 2πr^2, where A is the surface area, r is the radius, and h is the height.
Given that the radius of the cylindrical part is 0.9m and the height of the solid is 4.5m, we can calculate the surface area of the cylindrical part as follows:
A_cylinder = 2π(0.9)(4.5) + 2π(0.9)^2
A_cylinder ≈ 16.06 square meters (rounded to 1 decimal place)

Surface area of the conical part:
The surface area of a cone can be calculated using the formula A = πr(r + √(r^2 + h^2)), where A is the surface area, r is the radius, and h is the height.
Given that the radius of the conical part is 0.9m and the height of the conical part is 1.4m, we can calculate the surface area of the conical part as follows:
A_cone = π(0.9)(0.9 + √(0.9^2 + 1.4^2))
A_cone ≈ 7.78 square meters (rounded to 1 decimal place)

Total surface area of solid S:
To find the total surface area, we add the surface area of the cylindrical part and the surface area of the conical part:
A_total = A_cylinder + A_cone
A_total ≈ 16.06 + 7.78
A_total ≈ 23.84 square meters (rounded to 1 decimal place)

Now let's determine the height of the square base pillar with the same volume as solid S.

To find the height of the square base pillar, we need to set up an equation using the volumes of solid S and the pillar.

Let h_pillar be the height of the square base pillar.
Given that the volume of solid S is 12.18 cubic meters, we can set up the equation as follows:
1.6^2 * h_pillar = 12.18

Solving for h_pillar:
h_pillar = 12.18 / 1.6^2
h_pillar ≈ 4.8 meters (rounded to 1 decimal place)

Therefore, the height of the square base pillar is approximately 4.8 meters.