Hemispherical dome

What is the coverage area of the painting of a hemispherical dome with a diameter of 8 m?

Correct answer:

S =  100.531 m2

Step-by-step explanation:

D=8 m r=D/2=8/2=4 m  S0​  = 4 π r2 S = S0​/2  S=2π⋅ r2=2⋅ 3.1416⋅ 42=100.531 m2

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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.

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 Hemisphere
The 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 Formula
Substitute r = 4 m into the formula:

A = 2π (4)2.

Step 3:

Calculate r2
Calculate r2 :

r2 = 42 = 16.

Step 4:

Multiply by 2π
Now, multiply by 2π :

A = 2π × 16 = 32π.

Step 5:

Approximate the Area
If 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

or

100.53 m2







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