Question

Help me with the answer

Answer 1

From the figure sketched above:

l= slant height=16in

diameter=13in, so we need to get the radius

r=radius=diameter/2

`r=(13)/(2)=6.5in`

The figure above is a Cone.

`\text{Volume of the cone=}(1)/(3)\pi* r^2\sqrt[]{l^2-r^2}`
`\begin{gathered} V=(1)/(3)*3.14*6.5^2\sqrt[]{16^2-6.5^2} \\ V=(1)/(3)*3.14*42.25\sqrt[]{256-42.25} \\ V=(1)/(3)*3.14*42.25*\sqrt[]{213.75} \end{gathered}`
`\begin{gathered} V=(1)/(3)*3.14*42.25*14.62 \\ V=(1939.5623)/(3)=646.5208\approx646.52in^3 \end{gathered}`

Hence, the volume of the cone is 646.52in³.