Question

Find the volume of the cone to the nearest tenth.Use 3.14 for pi

Answer 1

The slant height of cone L=6.3ft

Base radius is5.9/2 =2.95ft

The volume of a cone is given by

`(1)/(3)\Pi r^2h`

where h= the vertical height of the cone, r=base radius

to find the vertical height, we use Pythagoras theorem

`\begin{gathered} l^2=h^2+r^2 \\ 6.3^2=h^2+2.95^2 \end{gathered}`
`\begin{gathered} 39.69=h^2+8.70 \\ h^2=39.69-8.70 \end{gathered}`
`\begin{gathered} h^2=30.99 \\ \text{taking the square root of both side} \\ h=5.57ft \end{gathered}`
`\text{volume of cone =}(1)/(3)*3.14*2.95^2*5.57`
`\begin{gathered} =(1)/(3)*3.14*8.70*5.57 \\ =(1)/(3)*152.16 \\ =50.72 \end{gathered}`

The volume of the cone is 51.0ft³

The right option is the Third one