Question

A hemisphere-shaped bowl with radius 1 foot is filled full with chocolate. All of the chocolate is then evenly distributed between 27 congruent, smaller hemisphere-shaped molds. What is the radius of each of the smaller molds, in feet

Answer 1

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.

How to calculate the volume of a hemisphere?

The volume of the hemisphere is calculated by using the formula,

= $\frac{2}{3}$ × π × r³ cubic units

where r is the radius of the hemisphere.

Calculation:

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 =  $\frac{2}{3}$ × π × (1)³

  =  $\frac{2}{3}$ × π cubic feets

The volume of each smaller hemisphere-shaped mold =  $\frac{2}{3}$ × π × r³ cubic units

So, for 27 molds, the volume = 27 × $\frac{2}{3}$ × π × r³ cubic units

All of the chocolate is then evenly distributed between 27 congruent, smaller hemisphere-shaped molds.

Then,

$\frac{2}{3}$ × π = 27 × $\frac{2}{3}$ × 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:

https://brainly.com/question/15975126

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