Question

Cones A and B both have volume 48(3.14) cubic units but they have different dimensions. Cone A has radius 6 units and height 4 units.

Part A

Find one possible radius and height for Cone B.
Radius: Height:

Part B
Explain how you know Cone B has the same volume as Cone A. ​

Answer 1

Part A r =
`6√(2)` units & h = 2 units:

Explanation:

Here we have , cones A and B both have volume 48(3.14) cubic units but they have different dimensions. Cone A has radius 6 units and height 4 units. We need to find:

Part A

Find one possible radius and height for Cone B.

Since , volume of cone A and B are same so ,

Volume of cone A =
`V_1` , Volume of cone V =
`V_2`

By hit & trial , One possible radius and height for Cone B is r =
`6√(2)` units & h = 2 units:

⇒
`V_2 = (1)/(3)\pi r^2h`

⇒
`V_2 = (1)/(3)(3.14) (6√(2))^2(2)`

⇒
`V_2 = 48units^3`

Part B

Explain how you know Cone B has the same volume as Cone A. ​

Volume of cone A =
`V_1` :

Cone A has radius 6 units and height 4 units, So

⇒
`V_1 = (1)/(3)\pi r^2h`

⇒
`V_1 = (1)/(3)(3.14) (6})^2(4)`

⇒
`V_2 = 48units^3`

Volume of cone V =
`V_2`

⇒
`V_2 = (1)/(3)\pi r^2h`

⇒
`V_2 = (1)/(3)(3.14) (6√(2))^2(2)`

⇒
`V_2 = 48units^3`

Hence, Volume of both are same!