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.
b. Calculate the total surface area of soild S.
just like the volume one, but you only have to find the lateral area of the cone, and skip the top base of the cylinder.
To calculate the total surface area of the solid S, we need to find the surface area of both the cylindrical part and the conical part, and then add them together.
Surface area of the cylindrical part:
The surface area of a cylinder is given by the formula A = 2πr(r + h), where A is the surface area, r is the radius, and h is the height. In this case, the height of the cylindrical part is 4.5m and the radius is 0.9m.
A_cylindrical = 2π(0.9)(0.9 + 4.5)
= 2π(0.9)(5.4)
= 9.72π m^2
Surface area of the conical part:
The surface area of a cone is given by the formula A = πr(r + l), where A is the surface area, r is the radius, and l is the slant height. In this case, the height of the conical part is 1.4m, the radius is 0.9m, and we need to find the slant height.
Using the Pythagorean theorem, we can find the slant height:
l^2 = r^2 + h^2
l^2 = (0.9)^2 + (1.4)^2
l^2 = 0.81 + 1.96
l^2 = 2.77
l = sqrt(2.77)
l ≈ 1.664 m
A_conical = π(0.9)(0.9 + 1.664)
= π(0.9)(2.564)
≈ 6.897π m^2
Total surface area:
To find the total surface area of the solid S, we add the surface area of the cylindrical part and the conical part together.
Total surface area = A_cylindrical + A_conical
= 9.72π + 6.897π
= 16.617π m^2
Therefore, the total surface area of solid S is approximately 16.617π square meters.