Understanding the Problem
To determine how many litres of milk a hemispherical bowl can hold, we need to calculate its volume. The volume of a hemisphere can be derived from the formula for the volume of a sphere.
Key Formula
- Volume of a sphere = (4/3) * π * r³
- Volume of a hemisphere = (1/2) * Volume of a sphere = (2/3) * π * r³
Finding the Radius
- The diameter of the bowl is given as 10.5 cm.
- Therefore, the radius (r) is half of the diameter:
- r = diameter / 2 = 10.5 cm / 2 = 5.25 cm
Calculating the Volume
- Now, we can substitute the radius into the volume formula:
- Volume = (2/3) * π * (5.25)³
Calculating (5.25)³
- 5.25³ = 144.703125 cm³ (approximately)
Calculating the Volume
- Volume = (2/3) * π * 144.703125
- Using π ≈ 3.14:
- Volume ≈ (2/3) * 3.14 * 144.703125 ≈ 303.96 cm³ (approximately)
Converting to Litres
- Since 1 litre = 1000 cm³:
- Volume in litres = 303.96 cm³ / 1000 = 0.30396 litres
Final Answer
- Therefore, the hemispherical bowl can hold approximately 0.304 litres of milk.