a hemispherical bowl with radius 25cm contains water whose depth is 10cm. what is the water's surface area
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To find the water's surface area in the hemispherical bowl, we need to calculate the area of the curved surface of the water.
The curved surface area of a hemisphere is given by the formula:
A = 2πr^2
Where:
A is the surface area
π is a mathematical constant approximately equal to 3.14159
r is the radius of the hemisphere
In this case, the radius of the bowl is given as 25 cm.
So, to find the surface area of the water, we need to adjust the radius to account for the depth of the water.
The depth is given as 10 cm. This means that only a portion of the hemisphere is filled with water. The water forms a smaller spherical cap inside the hemisphere.
To find the radius of the water's surface, we need to use the following equation:
r_water = r_bowl - depth
Substituting the values, we get:
r_water = 25 cm - 10 cm = 15 cm
Now, we can substitute the value of the water's radius into the formula to find the surface area:
A = 2πr_water^2
A = 2π(15 cm)^2
A ≈ 2π(225 cm^2)
A ≈ 2π(225 cm^2) ≈ 2 * 3.14159 * 225 cm^2 ≈1413.72 cm^2
Therefore, the water's surface area in the hemispherical bowl is approximately 1413.72 cm^2.