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

Answer:

12.8 cm

Step-by-step explanation:

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

It is given that after painting his porch Jamil has $\frac{1}{4}$ 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 $\text{Base area}\times\text{height}$

So, paint in the can $=\pi r^{2}\times h$

$=\pi (8)^{2}\times 20$

Now $\frac{1}{4}$  of the can is $\frac{1}{4}\times \pi (8)^{2}\times 20$

$=320\pi$ 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.

$\pi (5)^{2}\times h=320\pi$

$h=\frac{320\pi}{25\pi}$

$h=12.8$

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