Question

After painting his porch jamil has 1/4 of a can of paint remaining the can has a radius of 8cm and a height of 20cm he wants to pour the remaining paint into a smaller can for storage the smaller can has a radius of 5cm what does the height of the smaller can need to be to hold all the paint?

Answer 1

Answer:12.8

Step-by-step explanation:

becuase I said so

Answer 2

12.8 cm

Explanation:

Radius of the can is 8 cm and height is 20 cm.

It is given that after painting his porch Jamil has
`(1)/(4)` of a can of paint remaining. So, first we need to find the total amount of paint in the can.

Total amount of paint in the can is
`\text{Base area}*\text{height}`

So, paint in the can
`=\pi r^(2)* h`

`=\pi (8)^(2)* 20`

Now
`(1)/(4)` of the can is
`(1)/(4)* \pi (8)^(2)* 20`

`=320\pi` cubic cm.

Now, let the height of the smaller can be h cm.

Radius of the smaller can is 5 cm.

As, the paint is poured into the smaller can the volume of both the cans will be same.

`\pi (5)^(2)* h=320\pi`

`h=(320\pi)/(25\pi)`

`h=12.8`

Hence, height of the smaller can to hold the paint must be 12.8 cm.