Answer:
556 cm²
Step-by-step explanation:
You want the surface area of a cylinder of radius 5 cm, height 12 cm, topped with a cone of height 4 cm.
Area
The surface area of the figure will be ...
surface area = base area + cylinder lateral area + cone lateral area
Base area
The base is a circle of radius 5 cm, so its area is ...
A = πr² = π(5 cm)² = 25π cm²
Cylinder area
The lateral area of the cylinder is the product of its circumference and its height:
A = 2πrh = 2π(5 cm)(12 cm) = 120π cm²
Cone area
The lateral area of the cone is half the product of the circumference and its slant height. The slant height can be found using the Pythagorean theorem:
s² = r² + h²
s = √(5² +4²) = √(25 +16) = √41 . . . . cm (about 6.403 cm)
Then the lateral area of the cone is ...
LA = πrs
LA = π(5 cm)(√41 cm) = 5√41π cm² ≈ 32.016π cm²
Total surface area
This brings the total surface area to ...
surface area = 25π cm² +120π cm² +5√41·π cm² ≈ 556 cm²
The area of the composite solid is about 556 cm².
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