Find the percentage of waste material in converting a cylinder of base diameter 10 cm and height 20 cm into a cone of equal base, but double the height of the cylinder. A)25% b)20% c)35% d)33.3%
Answers
Answer:
33.3%
Step-by-step explanation:
To find the wasted material we find the volume of both figures
What they mean by wasted material is that the volume of the cone was volume of the cone is less than the volume of the cylinder.
The wasted material is the difference in volume between the cylinder and the cone.
We can now find the volume of the cylinder.
Volume = πr²h
The radius of the cylinder is 10cm ÷ 2 = 5 cm
10 is the diameter
22/7 × 5 × 5 × 20 = 1571.43 cm³
Then we have been told that the base is the same and the height was doubled meaning the height was
20 × 2 = 40 cm
The volume = ⅓πr²h
⅓ × 22/7 × 5 × 5 × 40 = 1047.62 cm³
We can therefore find the wasted because we have both the volumes
1571.43 - 1047.63 = 523.81 cm³
The volume of the cylinder is 100%.
To find the percentage of the wasted material
100% = 1571.43
523.81
100 × 523.81 = 52381
52381 ÷ 1571.43 = 33.3 %