Rocket Surface Area Calculation

To calculate the total surface area of the rocket, we need to find the surface area of the cylindrical part and the conical part separately, and then add them together.

Cylindrical Part:
The cylindrical part of the rocket is closed at the lower end, so we only need to consider the curved surface area. The formula for the curved surface area of a cylinder is given by:
Curved Surface Area of Cylinder = 2πrh

Where:
r = radius of the cylinder
h = height of the cylinder

In this case, the radius of the cylinder is not given directly. However, since the cylinder is attached to a cone of the same radius, we can assume that the radius of the cylinder is also 2.5 m.

Thus, the curved surface area of the cylindrical part is:
Curved Surface Area of Cylinder = 2π(2.5)(21)

Conical Part:
The conical part of the rocket is attached to the top of the cylindrical part. The formula for the surface area of a cone is given by:
Surface Area of Cone = πr(r + l)

Where:
r = radius of the cone
l = slant height of the cone

In this case, the radius of the cone is given as 2.5 m and the slant height is given as 8 m.

Thus, the surface area of the conical part is:
Surface Area of Cone = π(2.5)(2.5 + 8)

Total Surface Area:
To find the total surface area of the rocket, we add the surface area of the cylindrical part and the conical part:
Total Surface Area = Curved Surface Area of Cylinder + Surface Area of Cone

Calculate the values and add them to find the total surface area of the rocket.

Summary:
To calculate the total surface area of the rocket, we find the surface area of the cylindrical part and the conical part separately and then add them together. The curved surface area of the cylindrical part is found using the formula 2πrh, where r is the radius of the cylinder and h is the height of the cylinder. The surface area of the conical part is found using the formula πr(r + l), where r is the radius of the cone and l is the slant height of the cone. After calculating the values, we add the surface areas of both parts to find the total surface area of the rocket.