Find the surface area of the composite solid. Round your answer to the nearest hundredth.
1 answer:
The surface area of the composite solid is 579.84 square feet
<h3>How to determine the surface area of the solid?</h3>The composite solid that completes the question is added as an attachment
From the attached figure, we have the following figures:
- Rectangular prism
- Cylinder
The surface area of a rectangular prism is
A = 2(lw + lh + wh)
Using the dimensions of the prism, we have:
A = 2(6 * 11 + 6 * 8 + 8 * 11)
This gives
A = 404
The surface area of a cylinder is
A = 2πr^2 + 2πrh
Using the dimensions of the cylinder, we have:
A = 2 * 3.14 * 4^2 + 2 * 3.14 * 4 * 5
Evaluate
A = 226.08
The area of the circle between both shapes is
A = πr^2
This gives
A = 3.14 * 4^2
A = 50.24
The surface area of the composite solid is then calculated as:
Surface area = Area of rectangular prism + Area of cylinder - Area of circle
This gives
Surface area = 404 + 226.08 - 50.24
Evaluate
Surface area = 579.84
Hence, the surface area of the composite solid is 579.84 square feet
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Answer:
Part 1) Triangles ABC, DBG, DEF and BEH are similar
Part 2)
Step-by-step explanation:
Part 1)
we know that
If two triangles are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent
In this problem Triangles ABC, DBG, DEF and BEH are similar, because its corresponding angles are congruent by AA Similarity Theorem
Part 2)
Remember that
If two triangles are similar, then the ratio of its corresponding sides is equal
therefore