Hemispherical dome
What is the coverage area of the painting of a hemispherical dome with a diameter of 8 m?
Correct answer:
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Dr. Math
To determine the coverage area of the painting of a hemispherical dome, we need to calculate the surface area of the hemisphere. The surface area of a hemisphere includes the curved surface area (half of a sphere) and the base area (a circle). However, since the dome is being painted, we will only consider the curved surface area.
- Diameter of the dome, d = 8 m .
- Radius of the dome, r = d2 = 82 = 4 m .
The curved surface area A of a hemisphere is given by:
where:
- r is the radius of the hemisphere,
- π is a constant (approximately 3.1416 ).
Substitute r = 4 m into the formula:
Calculate r2 :
Now, multiply by 2π :
If we use π ≈ 3.1416 , the area is:
The coverage area of the painting of the hemispherical dome is:
Given Data:
- Diameter of the dome, d = 8 m .
- Radius of the dome, r = d2 = 82 = 4 m .
Step 1:
Recall the Formula for the Curved Surface Area of a HemisphereThe curved surface area A of a hemisphere is given by:
A = 2π r2,
where:
- r is the radius of the hemisphere,
- π is a constant (approximately 3.1416 ).
Step 2:
Substitute the Radius into the FormulaSubstitute r = 4 m into the formula:
A = 2π (4)2.
Step 3:
Calculate r2Calculate r2 :
r2 = 42 = 16.
Step 4:
Multiply by 2πNow, multiply by 2π :
A = 2π × 16 = 32π.
Step 5:
Approximate the AreaIf we use π ≈ 3.1416 , the area is:
A ≈ 32 × 3.1416 = 100.53 m2.
Final Answer:
The coverage area of the painting of the hemispherical dome is:
32π m2
or100.53 m2
You need to know the following knowledge to solve this word math problem:
solid geometryplanimetricsGrade of the word problem
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