Answer:
Volume of the cone in ascending order.
![V_{2}=270\pi\ units^{3}](https://tex.z-dn.net/?f=V_%7B2%7D%3D270%5Cpi%5C%20units%5E%7B3%7D%3CV_%7B3%7D%3D300%5Cpi%5C%20units%5E%7B3%7D%3CV_%7B4%7D%3D363%5Cpi%5C%20units%5E%7B3%7D%3CV_%7B1%7D%3D400%5Cpi%5C%20units%5E%7B3%7D)
cone with DIAMETER of 18 & height of 10
cone with RADIUS of 10 & height of 9
cone with RADIUS of 11 & height of 9
cone with DIAMETER of 20 & height of 12
Step-by-step explanation:
Let
be the volume of the cone.
Let d, r and h be the diameter, radius and height of the cone.
Given:
![d_{1} = 20\ and\ h_{1}=12](https://tex.z-dn.net/?f=d_%7B1%7D%20%3D%2020%5C%20and%5C%20h_%7B1%7D%3D12)
![d_{2} = 18\ and\ h_{2}=10](https://tex.z-dn.net/?f=d_%7B2%7D%20%3D%2018%5C%20and%5C%20h_%7B2%7D%3D10)
![r_{3} = 10\ and\ h_{3}=9](https://tex.z-dn.net/?f=r_%7B3%7D%20%3D%2010%5C%20and%5C%20h_%7B3%7D%3D9)
![r_{4} = 11\ and\ h_{14}=9](https://tex.z-dn.net/?f=r_%7B4%7D%20%3D%2011%5C%20and%5C%20h_%7B14%7D%3D9)
Arrange the cones in order from lease volume to greatest volume.
Solution:
The volume of the cone is given below.
----------------(1)
where: r is radius of the base of cone.
and h is height of the cone.
The volume of the cone for ![d_{1} = 20\ and\ h_{1}=12](https://tex.z-dn.net/?f=d_%7B1%7D%20%3D%2020%5C%20and%5C%20h_%7B1%7D%3D12)
![r_{1} = \frac{d_{1}}{2}](https://tex.z-dn.net/?f=r_%7B1%7D%20%3D%20%5Cfrac%7Bd_%7B1%7D%7D%7B2%7D)
![r_{1} = \frac{20}{2}=10\ units](https://tex.z-dn.net/?f=r_%7B1%7D%20%3D%20%5Cfrac%7B20%7D%7B2%7D%3D10%5C%20units)
![V_{1}=\pi (r_{1})^{2} \frac{h_{1}}{3}](https://tex.z-dn.net/?f=V_%7B1%7D%3D%5Cpi%20%28r_%7B1%7D%29%5E%7B2%7D%20%5Cfrac%7Bh_%7B1%7D%7D%7B3%7D)
![V_{1}=\pi (10)^{2} \frac{12}{3}](https://tex.z-dn.net/?f=V_%7B1%7D%3D%5Cpi%20%2810%29%5E%7B2%7D%20%5Cfrac%7B12%7D%7B3%7D)
![V_{1}=\pi\times 100\times 4](https://tex.z-dn.net/?f=V_%7B1%7D%3D%5Cpi%5Ctimes%20100%5Ctimes%204)
![V_{1}=400\pi\ units^{3}](https://tex.z-dn.net/?f=V_%7B1%7D%3D400%5Cpi%5C%20units%5E%7B3%7D)
Similarly, for volume of the cone for ![d_{2} = 18\ and\ h_{2}=10](https://tex.z-dn.net/?f=d_%7B2%7D%20%3D%2018%5C%20and%5C%20h_%7B2%7D%3D10)
![r_{2} = \frac{d_{2}}{2}](https://tex.z-dn.net/?f=r_%7B2%7D%20%3D%20%5Cfrac%7Bd_%7B2%7D%7D%7B2%7D)
![r_{2} = \frac{18}{2}=9\ units](https://tex.z-dn.net/?f=r_%7B2%7D%20%3D%20%5Cfrac%7B18%7D%7B2%7D%3D9%5C%20units)
![V_{2}=\pi (r_{2})^{2} \frac{h_{2}}{3}](https://tex.z-dn.net/?f=V_%7B2%7D%3D%5Cpi%20%28r_%7B2%7D%29%5E%7B2%7D%20%5Cfrac%7Bh_%7B2%7D%7D%7B3%7D)
![V_{2}=\pi (9)^{2} \frac{10}{3}](https://tex.z-dn.net/?f=V_%7B2%7D%3D%5Cpi%20%289%29%5E%7B2%7D%20%5Cfrac%7B10%7D%7B3%7D)
![V_{2}=\pi\times 81\times \frac{10}{3}](https://tex.z-dn.net/?f=V_%7B2%7D%3D%5Cpi%5Ctimes%2081%5Ctimes%20%5Cfrac%7B10%7D%7B3%7D)
![V_{2}=\pi\times 27\times 10](https://tex.z-dn.net/?f=V_%7B2%7D%3D%5Cpi%5Ctimes%2027%5Ctimes%2010)
![V_{2}=270\pi\ units^{3}](https://tex.z-dn.net/?f=V_%7B2%7D%3D270%5Cpi%5C%20units%5E%7B3%7D)
Similarly, for volume of the cone for ![r_{3} = 10\ and\ h_{3}=9](https://tex.z-dn.net/?f=r_%7B3%7D%20%3D%2010%5C%20and%5C%20h_%7B3%7D%3D9)
![V_{3}=\pi (r_{3})^{2} \frac{h_{3}}{3}](https://tex.z-dn.net/?f=V_%7B3%7D%3D%5Cpi%20%28r_%7B3%7D%29%5E%7B2%7D%20%5Cfrac%7Bh_%7B3%7D%7D%7B3%7D)
![V_{3}=\pi (10)^{2} \frac{9}{3}](https://tex.z-dn.net/?f=V_%7B3%7D%3D%5Cpi%20%2810%29%5E%7B2%7D%20%5Cfrac%7B9%7D%7B3%7D)
![V_{3}=\pi\times 100\times 3](https://tex.z-dn.net/?f=V_%7B3%7D%3D%5Cpi%5Ctimes%20100%5Ctimes%203)
![V_{3}=\pi\times 300](https://tex.z-dn.net/?f=V_%7B3%7D%3D%5Cpi%5Ctimes%20300)
![V_{3}=300\pi\ units^{3}](https://tex.z-dn.net/?f=V_%7B3%7D%3D300%5Cpi%5C%20units%5E%7B3%7D)
Similarly, for volume of the cone for ![r_{4} = 11\ and\ h_{4}=9](https://tex.z-dn.net/?f=r_%7B4%7D%20%3D%2011%5C%20and%5C%20h_%7B4%7D%3D9)
![V_{4}=\pi (r_{4})^{2} \frac{h_{4}}{3}](https://tex.z-dn.net/?f=V_%7B4%7D%3D%5Cpi%20%28r_%7B4%7D%29%5E%7B2%7D%20%5Cfrac%7Bh_%7B4%7D%7D%7B3%7D)
![V_{4}=\pi (11)^{2} \frac{9}{3}](https://tex.z-dn.net/?f=V_%7B4%7D%3D%5Cpi%20%2811%29%5E%7B2%7D%20%5Cfrac%7B9%7D%7B3%7D)
![V_{4}=\pi\times 121\times 3](https://tex.z-dn.net/?f=V_%7B4%7D%3D%5Cpi%5Ctimes%20121%5Ctimes%203)
![V_{4}=\pi\times 363](https://tex.z-dn.net/?f=V_%7B4%7D%3D%5Cpi%5Ctimes%20363)
![V_{4}=363\pi\ units^{3}](https://tex.z-dn.net/?f=V_%7B4%7D%3D363%5Cpi%5C%20units%5E%7B3%7D)
So, the volume of the cone in ascending order.
![V_{2}=270\pi\ units^{3}](https://tex.z-dn.net/?f=V_%7B2%7D%3D270%5Cpi%5C%20units%5E%7B3%7D%3CV_%7B3%7D%3D300%5Cpi%5C%20units%5E%7B3%7D%3CV_%7B4%7D%3D363%5Cpi%5C%20units%5E%7B3%7D%3CV_%7B1%7D%3D400%5Cpi%5C%20units%5E%7B3%7D)