I need help!!!
a hemispherical bowl with radius 25cm contains water whose depth is 10cm. what is the water's surface area
I could also use the formula of a sphere
Oh, water you talking about? Let me calculate it for you.
The surface area of the water in the hemispherical bowl can be calculated using the formula for the surface area of a hemisphere, which is 2πr^2, where r is the radius of the hemisphere.
In this case, the radius of the hemisphere is 25 cm, so we can substitute that into the formula:
Surface area = 2π(25)^2 = 2π(625) = 1250π cm^2
So, the surface area of the water is 1250π cm^2.
To find the water's surface area, we need to calculate the curved surface area of the hemispherical bowl up to the water level.
1. Calculate the curved surface area of the hemispherical bowl:
The formula for the curved surface area of a hemisphere is given by: A = 2πr², where r is the radius of the hemisphere.
In this case, the radius is 25 cm.
So, plug in the values into the formula:
A = 2π(25²)
A = 2π(625)
A ≈ 3.14 × 625
A ≈ 1962.5 cm²
2. Calculate the surface area of the water:
The surface area of the water will be the curved surface area of the hemisphere up to the water level. Since the depth of the water is 10 cm, we need to find the surface area for a segment of 10 cm in height.
The formula for the surface area of a spherical segment is given by: A = 2πrh, where r is the radius of the sphere and h is the height of the segment.
In this case, r is 25 cm and h is 10 cm.
So, plug in the values into the formula:
A = 2π(25)(10)
A = 2π(250)
A ≈ 3.14 × 250
A ≈ 785 cm²
Therefore, the water's surface area is approximately 785 cm².
To find the surface area of the water in a hemispherical bowl, we need to calculate the curved surface area (CSA) and the circular base area.
1. Curved Surface Area (CSA):
The CSA is the area of the water's surface on the inside of the bowl. Since it is a hemisphere, the CSA is equal to half the surface area of a sphere with the same radius.
The formula for the surface area of a sphere is given by:
A = 4πr^2
Therefore, the CSA of a hemisphere with radius r is:
CSA = (1/2) * 4πr^2
= 2πr^2
2. Circular Base Area:
The base of the water is the circular shape formed by the bottom of the bowl. It has the same radius as the hemisphere.
The formula for the area of a circle is given by:
A = πr^2
Now, let's calculate the surface area of the water.
Surface Area = CSA + Circular Base Area
= 2πr^2 + πr^2
= 3πr^2
Given that the radius, r, is 25cm, we can substitute it into the formula to find the surface area of the water.
Surface Area = 3π(25)^2
= 3π(625)
= 1875π cm^2
Therefore, the surface area of the water in the hemispherical bowl is 1875π cm^2, where π is approximately 3.14159.
equation of circle radius 25 :
x^2 + y^2 = 25^2 = 625
now what is x when 15 cm from center (which is ten cm from surface)?
x^2 + 225 = 625
x^2 = 400
x = 20
that is our radius at urface
area = pi (20)^2 = 400 pi = 1257 cm^2