Question

28. Four cones have the dimensions shown below. Figure 1 Figure 2 Figure 3 Figure 4 14 in. 13 in. 10 in. 12 in 8 in. 9 In. 7 In. 6 In. Sort the cones from least to greatest volume Round to the nearest tenth. Figure Volume (in) Least Greatest

Answer 1

Consider that the Volume of a cone (V), which has a height (h) and radius (r) is given by,

`V=(1)/(3)\pi r^2h`

Figure-1

Given that the radius is 8 in. and the height is 14 in. the volume is calculated as,

`\begin{gathered} V_1=(1)/(3)\pi(8)^2(14) \\ V_1=(896)/(3)\pi \\ V_1=938.289 \end{gathered}`

So the volume of this cone is 938.289 cubic inches approximately.

Figure-2

Given that the radius is 9 in. and the height is 13 in. the volume is calculated as,

`\begin{gathered} V_2=(1)/(3)\pi(9)^2(13) \\ V_2=351\pi \\ V_2=1102.699 \end{gathered}`

So the volume of this cone is 1102.699 cubic inches approximately.

Figure-3

Given that the radius is 7 in. and the height is 10 in. the volume is calculated as,

`\begin{gathered} V_3=(1)/(3)\pi(7)^2(10) \\ V_3=(490)/(3)\pi \\ V_3=513.127 \end{gathered}`

So the volume of this cone is 513.127 cubic inches approximately.

Figure-4

Given that the radius is 6 in. and the height is 12 in. the volume is calculated as,

`\begin{gathered} V_4=(1)/(3)\pi(6)^2(12) \\ V_4=144\pi \\ V_4=452.389 \end{gathered}`

So the volume of this cone is 1102.699 cubic inches approximately.

Observe the volume values obtained for all four cones,

[tex]\begin{gathered} 452.389<513.127<938.289<1102.699 \\ \Rightarrow V_4Thus, the order of least to greatest volume is, figures 4, 3, 1, 2 respectively.