Answer:
200π cm².
Explanation:
To find the total surface area of the solid made from a cone and a cylinder, we need to calculate the surface area of each component separately and then add them together.
1. Surface area of the cone:
The surface area of a cone can be calculated using the formula: πr(r + l), where r is the radius of the base and l is the slant height.
Given that the radius of the cone is 5 cm and the slant height is 11 cm, we can substitute these values into the formula to find the surface area of the cone.
Surface area of the cone = π(5)(5 + 11) = 80π cm²
2. Surface area of the cylinder:
The surface area of a cylinder can be calculated using the formula: 2πrh + 2πr², where r is the radius of the base and h is the height.
Given that the radius of the cylinder is also 5 cm and the height is 7 cm, we can substitute these values into the formula to find the surface area of the cylinder.
Surface area of the cylinder = 2π(5)(7) + 2π(5)² = 70π + 50π = 120π cm²
3. Total surface area:
To find the total surface area of the solid, we add the surface area of the cone to the surface area of the cylinder.
Total surface area = Surface area of the cone + Surface area of the cylinder
Total surface area = 80π + 120π
Total surface area = 200π cm²
Therefore, the total surface area of the solid, including the base, in terms of pi is 200π cm².