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Find the surface area of the composite solids. Tip do not use the traditional formulas as some of the parts of the solids are not included in the surface area. Round your answer to the nearest whole number if necessary.

Find the surface area of the composite solids. Tip do not use the traditional formulas-example-1
User Dan Dinu
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1 Answer

3 votes

Answer:

556 cm²

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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User Alexander Soare
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