Answer:
(162π + 144) cm² ≈ 652.9 cm²
Explanation:
You want to find the surface area of a cylinder from which a 1/4 longitudinal sector has been removed.
Surface area
The surfaces that make up the outside area of the figure are ...
- two bases, each a 3/4 circle of radius 6 cm
- 3/4 of the lateral area of a cylinder of 6 cm radius, 12 cm high
- 2 rectangles that are 6 cm by 12 cm.
The appropriate formulas can be used to find the areas of each of these, and the areas can be summed to get the total surface area.
Bases
The area of a circle with 6 cm radius is ...
A = πr²
A = π(6 cm)² = 36π cm²
The area of one 3/4 circle is ...
base area = (3/4)(36π cm²) = 27π cm²
The area of both bases is twice this:
total base area = 2×(27π cm²) = 54π cm²
Curved surface
The lateral area of a cylinder of radius 6 cm and height 12 cm is ...
A = 2πrh
A = 2π(6 cm)(12 cm) = 144π cm²
The curved surface of this figure is 3/4 of this area:
curved surface area = 3/4×(144π cm²) = 108π cm²
Rectangular area
The area of the two rectangles is ...
A = bh . . . . times 2
A = 2(6 cm)(12 cm) = 144 cm²
Total area
The total area of the cut cylinder is ...
total area = total base area + curved surface area + rectangular area
total area = 54π cm² +108π cm² + 144 cm²
total area = (162π + 144) cm² ≈ 652.9 cm²
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Additional comment
You can also regard the surface area as 3/4 of the area of a cylinder, plus the area of two rectangles:
(3/4)(2πr)(r+h) + 2rh = (3/4)(12π)(18) +2(6)(12) = 162π +144