MATH SOLVE

5 months ago

Q:
# after painting his porch jamil had a 1/4 can of paint left the radius of the can is 8 cm and the height is 20 cm he wants to put the remaining paint into a smaller can with a radius of 5 cm what does the height of the smaller can need to be to hold all the paint.

Accepted Solution

A:

Answer:The height of small can need to be 12.8 cm to hold all the paintStep-by-step explanation:- Jamil had a 1/4 can of paint left- The radius of the can is 8 cm and its height is 20 cm- He wants to put the remaining paint into a smaller can with a radius of 5 cm - We need to find the height of the smaller can- The volume of the paint in the larger can is the same volume of paint will put in the smaller can- Lets find the volume of the paint in the larger can∵ The volume of the paint in the larger can = 1/4 its volume∵ The can is shaped a cylinder∵ Volume the cylinder = πr²h, where r is the radius of it and h its height∵ r = 8 cm and h = 20 cm∴ The volume of the paint = [tex]\frac{1}{4}\pi (8)^{2}(20)=320\pi[/tex] cm³- Same amount of paint will put in the smaller can ∵ r = 5 cm and V = 320π cm³∴ 320π = π(5)²h- Divide both sides by π∴ 320 = 25 h- divide both sides by 25∴ h = 12.8 cm* The height of small can need to be 12.8 cm to hold all the paint