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I need to find the area of this cylinder can you help me

I need to find the area of this cylinder can you help me-example-1

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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

User Michael Hillman
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