Final answer:
To calculate the volume of cake batter in a hemispherical mixing bowl, use the volume formula for a spherical cap, which accounts for the depth being less than the radius. The standard volume formula for a full sphere (¾πr³) and for a hemisphere (½(¾πr³)) do not apply directly here.
Step-by-step explanation:
To calculate the volume of cake batter in a hemispherical mixing bowl of radius r cm and h cm deep, we must use the volume formula for a hemisphere, which is a fraction of the volume formula for a sphere. The volume of a full sphere is given by ¾πr³, so the volume of a hemisphere would be half of that, ½(¾πr³).
However, if the bowl is only filled to a depth of h cm, which is less than the radius, we are dealing with a spherical cap. The volume V of a spherical cap can be calculated using the formula: V = πh²(½r - ¼ h). When simplified, this formula reflects the volume for the segment of a sphere.
In the specific example provided, where the formula for a cylinder V = πr²h is used to calculate the volume of 9.278 cm³ for a depth of 5.25 cm and radius of 0.750 cm, this formula is applicable for cylindrical shapes or the segment of a cylinder, not a hemisphere. For the student's question regarding the hemispherical mixing bowl, we need to use the corrected formula as above that is specific to spherical segments or caps, not the cylindrical volume formula.