Find the depth in meters of a hemispherical bowl that will hold 12.75kg of water
since volume = weight/density, look up the density d of water (in kg/m^3) and solve for r.
2/3 πr^3 = 12.75/d
What is the depth
To find the depth of a hemispherical bowl that will hold 12.75 kg of water, we need to use the formula for the volume of a hemisphere and the density of water.
Step 1: Determine the density of water.
The density of water is approximately 1000 kg/m³.
Step 2: Calculate the volume of water.
The formula for the volume of a hemisphere is:
V = (2/3) * π * r³,
where V is the volume and r is the radius.
We need to find the radius of the hemispherical bowl first. Since the bowl is only half of a complete sphere (hemisphere), we divide the volume of water by 2. So,
V = (2/3) * π * r³ / 2.
12.75 kg of water has the same volume as 12.75 L (since the density of water is approximately 1000 kg/m³).
V = 12.75 L.
Converting liters to cubic meters (1 L = 0.001 m³):
V = 12.75 * 0.001 m³ = 0.01275 m³.
Now we can set up the equation and solve for the radius:
0.01275 = (2/3) * π * r³ / 2.
Step 3: Solve for the radius.
Multiply both sides by 2/(2/3) to cancel the fraction:
0.01275 * (2/2/3) = π * r³.
0.01275 * (3/2) = π * r³.
0.019125 = π * r³.
Divide both sides by π:
r³ = 0.019125 / π.
r³ ≈ 0.006105.
Take the cube root of both sides to find the radius:
r ≈ ∛0.006105.
r ≈ 0.1638 meters.
Step 4: Calculate the depth.
Since the depth is the same as the radius in a hemisphere, the depth of the hemispherical bowl is approximately 0.1638 meters or 16.38 centimeters.
To find the depth of a hemispherical bowl that will hold a certain amount of water, we need to use the equation for the volume of a hemisphere and the density of water. Here's how you can solve it:
1. Start by finding the volume of water in liters. We know that 1 kilogram of water is equal to 1 liter, so the volume of water in liters will be the same as its mass in kilograms. In this case, the volume is 12.75 liters.
2. The volume of a hemisphere can be calculated using the formula V = (2/3) * π * r^3, where V is the volume and r is the radius of the hemisphere.
3. Rearrange the formula to solve for the radius: r = cuberoot((3V) / (2π)).
4. Since we want to find the depth, which is the distance from the top of the bowl to the water surface, we need to subtract the radius from the height of the hemisphere. Half of the sphere's diameter is equal to the radius.
5. Finally, convert the depth from centimeters to meters by dividing by 100.
Let's plug in the values and calculate it:
V = 12.75 liters = 12.75 * 1000 = 12750 cm^3
r = cuberoot((3 * 12750) / (2 * π)) ≈ 12.75 cm
depth = radius / 100 = 12.75 / 100 = 0.1275 meters
Therefore, the depth of the hemispherical bowl that will hold 12.75 kg of water is approximately 0.1275 meters.