A glass dome covers a pool making an indoor Waterpark. If the height of the dome is 30 feet then what is the surface area of the glass dome? Round to the nearest tenth
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To find the surface area of the glass dome, we need to calculate the area of each individual side and then add them together. Since the dome is in the shape of a half-sphere, it consists of two parts: the curved part and the circular base.
Let's calculate the surface area step by step:
1. Calculate the curved part:
The curved part of the dome represents a half-sphere, with a height of 30 feet. To find the surface area of a sphere, we use the formula: A = 2πr², where A is the surface area and r is the radius.
Since we have the height of the dome, we can find the radius using the formula: r = h/2, where h is the height of the dome. Thus, the radius of the dome is 30/2 = 15 feet.
Substituting the radius into the formula, we get: A_curved = 2 * π * (15)^2.
2. Calculate the circular base:
The circular base of the dome is a circle with a radius equal to the radius of the dome. So, we can directly use the formula for the area of a circle: A = πr².
Substituting the radius (15 feet) into the formula, we get: A_base = π * (15)^2.
3. Calculate the total surface area:
To find the total surface area, we need to add the surface area of the curved part (A_curved) and the area of the circular base (A_base): Total Surface Area = A_curved + A_base.
Calculating the values and rounding to the nearest tenth:
A_curved = 2 * π * (15)^2 = 2 * 3.14 * (15)^2 ≈ 1413.7 square feet.
A_base = π * (15)^2 = 3.14 * (15)^2 ≈ 706.5 square feet.
Total Surface Area ≈ A_curved + A_base = 1413.7 + 706.5 ≈ 2120.3 square feet.
Therefore, the surface area of the glass dome is approximately 2120.3 square feet (rounded to the nearest tenth).