Question

Arrange the cones in order from lease volume to greatest volume

cone with DIAMETER of 20 & height of 12

cone with DIAMETER of 18 & height of 10

cone with RADIUS of 10 & height of 9

cone with RADIUS of 11 & height of 9

Answer 1

Volume of the cone in ascending order.

`V_(2)=270\pi\ units^(3)<V_(3)=300\pi\ units^(3)<V_(4)=363\pi\ units^(3)<V_(1)=400\pi\ units^(3)`

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

Explanation:

Let
`V_(2). V_(3). and\  V_(4).` 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`

`d_(2) = 18\ and\ h_(2)=10`

`r_(3) = 10\ and\ h_(3)=9`

`r_(4) = 11\ and\ h_(14)=9`

Arrange the cones in order from lease volume to greatest volume.

Solution:

The volume of the cone is given below.

`V=\pi r^(2) (h)/(3)`----------------(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`

`r_(1) = (d_(1))/(2)`

`r_(1) = (20)/(2)=10\ units`

`V_(1)=\pi (r_(1))^(2) (h_(1))/(3)`

`V_(1)=\pi (10)^(2) (12)/(3)`

`V_(1)=\pi* 100* 4`

`V_(1)=400\pi\ units^(3)`

Similarly, for volume of the cone for
`d_(2) = 18\ and\ h_(2)=10`

`r_(2) = (d_(2))/(2)`

`r_(2) = (18)/(2)=9\ units`

`V_(2)=\pi (r_(2))^(2) (h_(2))/(3)`

`V_(2)=\pi (9)^(2) (10)/(3)`

`V_(2)=\pi* 81* (10)/(3)`

`V_(2)=\pi* 27* 10`

`V_(2)=270\pi\ units^(3)`

Similarly, for volume of the cone for
`r_(3) = 10\ and\ h_(3)=9`

`V_(3)=\pi (r_(3))^(2) (h_(3))/(3)`

`V_(3)=\pi (10)^(2) (9)/(3)`

`V_(3)=\pi* 100* 3`

`V_(3)=\pi* 300`

`V_(3)=300\pi\ units^(3)`

Similarly, for volume of the cone for
`r_(4) = 11\ and\ h_(4)=9`

`V_(4)=\pi (r_(4))^(2) (h_(4))/(3)`

`V_(4)=\pi (11)^(2) (9)/(3)`

`V_(4)=\pi* 121* 3`

`V_(4)=\pi* 363`

`V_(4)=363\pi\ units^(3)`

So, the volume of the cone in ascending order.

`V_(2)=270\pi\ units^(3)<V_(3)=300\pi\ units^(3)<V_(4)=363\pi\ units^(3)<V_(1)=400\pi\ units^(3)`