The domain for f(x) and g(x) is the set of all real numbers.
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The radius of each of the smaller molds is r = 1/3 ft. Using the volume of the given hemisphere, the required radius is calculated.
<h3>How to calculate the volume of a hemisphere?</h3>The volume of the hemisphere is calculated by using the formula,
= × π × r³ cubic units
where r is the radius of the hemisphere.
<h3>Calculation:</h3>It is given that,
A hemisphere-shaped bowl with a radius r = 1 ft is filled with chocolate.
So, the volume of the bowl is
V = × π × (1)³
= × π cubic feets
The volume of each smaller hemisphere-shaped mold = × π × r³ cubic units
So, for 27 molds, the volume = 27 × × π × r³ cubic units
All of the chocolate is then evenly distributed between 27 congruent, smaller hemisphere-shaped molds.
Then,
× π = 27 ×
× π × r³
⇒ r³ = 1/27
⇒ r = 1/3 ft
Therefore, the required radius of each of the smaller molds is 1/3 foot.
Learn more about the volume of a hemisphere here:
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