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Answer:
The height of small can need to be 12.8 cm to hold all the paint
Step-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
The height of the smaller can need to be to hold all the paint will be 12.8 cm.The term height is frequently used to describe someone's or something's height.
What is the height?
Height is defined as the vertical distance between an object's top and bottom. It is measured in centimeters, millimeters, meters, and other units.
From the given conditions;
The volume of the paint in the larger can is,[tex]\rm V_L[/tex]
The volume of the paint in the smaller can is,[tex]\rm V_S[/tex]
The volume of the cylinder is, V
The radius of the can is,r= 8 cm
The height is,h=20 cm
The volume of the paint in the larger can is found as;
[tex]\rm V_L = \frac{1}{4} V \\\\ V=\pi r^2 h \\\\ V_L= \frac{1}{4} \pi (8)^2 (20) \\\\ V_L = 320 \pi \ cm^3[/tex]
The volume of the larger can is equal to the volume of the smaller can;
[tex]\rm V_S = V_L \\\\ 320 \ \pi \ cm^3=\pi r^2 h \\\\ \pi \ cm^3=\pi (5)^2 h \\\\ 320=25h \\\\ h =12.8 \ cm[/tex]
Hence the height of the smaller can need to be to hold all the paint will be 12.8 cm.
To learn more about the height refer to the link;
https://brainly.com/question/10726356
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