Question

cones a and b both have volume 48pi cubic units, but have different dimensions. cone a has radius 6 units and height 4 units. find one possible radius and height for cone b. explain how you know come b has the same volume as cone a

Answer 1

see the explanation

Explanation:

we know that

The volume of a cone is equal to

`V=(1)/(3)\pi r^(2)h`

`V=48\pi\ units^3`

so

`48\pi=(1)/(3)\pi r^(2)h`

Simplify

`144=r^(2)h` ----> equation A

step 1

Cone a

`r_a=6\ units\\h_a=4\ units`

Verify

substitute the given values in equation A

`144=r^(2)h`

`144=6^(2)(4)`

`144=144` ---> is true

step 2

Cone b

Assume the value of the radius and with the equation A calculate the value of the height

so

For
`r=5\ units`

substitute in the equation A

`144=r^(2)h`

`144=5^(2)h`

solve for h

`144=25h`

`h=5.76\ units`

Verify

substitute the given values in equation A

`144=r^(2)h`

`144=5^(2)(5.76)`

`144=144` ---> is true

The value of r and h satisfy the equation A, that means the volume of cone b is the same that volume of cone a