Question

a snowman is made of three spherical snowballs with a diameters of 3 feet, 2 feet, and 1 foot. what is the total volume of the snowman?represent your answer in terns of pi

Answer 1

The total volume of the snowman is
`6\pi\ ft^(3)`

Explanation:

we know that

The volume of a sphere is equal to

`V=(4)/(3)\pi r^(3)`

step 1

Find the volume of the spherical snowball with a diameter of 3 feet

Find the radius

`r=3/2=1.5\ ft` ----> the radius is half the diameter

substitute

`V=(4)/(3)\pi (1.5)^(3)`

`V1=(9)/(2)\pi\ ft^(3)`

step 2

Find the volume of the spherical snowball with a diameter of 2 feet

Find the radius

`r=2/2=1\ ft` ----> the radius is half the diameter

substitute

`V=(4)/(3)\pi (1)^(3)`

`V2=(4)/(3)\pi\ ft^(3)`

step 3

Find the volume of the spherical snowball with a diameter of 1 feet

Find the radius

`r=1/2=0.5\ ft` ----> the radius is half the diameter

substitute

`V=(4)/(3)\pi (0.5)^(3)`

`V3=(1)/(6)\pi\ ft^(3)`

step 4

Find the total volume

`V=V1+V2+V3`

substitute the values

`V=(9)/(2)\pi+(4)/(3)\pi+(1)/(6)\pi=(27+8+1)/(6)\pi=6\pi\ ft^(3)`