Step 1: Convert the diameter to radius
The diameter of the hemisphere is 10.5 cm. The radius \( r \) is half of the diameter: \[ r = \frac{10.5}{2} = 5.25 \, \text{cm} \]
Step 2: Volume of a Hemisphere
The formula for the volume \( V \) of a hemisphere is: \[ V = \frac{2}{3} \pi r^3 \] Substituting \( r = 5.25 \) cm: \[ V = \frac{2}{3} \pi (5.25)^3 \] First, calculate \( (5.25)^3 \): \[ (5.25)^3 = 145.5 \] Now calculate the volume: \[ V = \frac{2}{3} \times 3.1416 \times 145.5 \approx \frac{2}{3} \times 456.19 \approx 304.13 \, \text{cm}^3 \]
Step 3: Convert cm³ to Liters
1 liter = 1000 cm³, so to convert the volume from cm³ to liters, we divide by 1000: \[ V_{\text{liters}} = \frac{304.13}{1000} \approx 0.304 \, \text{liters} \]
The hemispherical bowl can hold approximately \( 0.304 \) liters of milk.