3. A balancing balloon toy is in the shape of a hemisphere (half-sphere) attached to the base of a cone. If the toy is 4ft tall and 2ft wide, what is the volume of the toy? Round your answer to two decimal places.

The volume of the toy is

Step-by-step explanation:

step 1

Find the volume of the hemisphere

The volume of the hemisphere is given by the formula

In this problem, the wide of the toy is equal to the diameter of the hemisphere

so

----> the radius is half the diameter

substitute

step 2

Find the volume of the cone

The volume of the cone is given by

we know that

The radius of the cone is the same that the radius of the hemisphere

so

The height of the cone is equal to subtract the radius of the hemisphere from the height of the toy

substitute the given values

step 3

Find the volume of the toy

we know that

The volume of the toy, is equal to the volume of the cone plus the volume of the hemisphere.

so

assume

the function makes a strait line horizontally with no x intercept but a y intercept at 9.