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 [tex]\frac{1}{4}[/tex] 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 [tex]\text{Base area}\times\text{height}[/tex]
So, paint in the can [tex]=\pi r^{2}\times h[/tex]
[tex]=\pi (8)^{2}\times 20[/tex]
Now [tex]\frac{1}{4}[/tex] of the can is [tex]\frac{1}{4}\times \pi (8)^{2}\times 20[/tex]
[tex]=320\pi [/tex] 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.
[tex]\pi (5)^{2}\times h=320\pi[/tex]
[tex]h=\frac{320\pi}{25\pi}[/tex]
[tex]h=12.8[/tex]
Hence, height of the smaller can to hold the paint must be 12.8 cm.
