Question

The volume of this cone is 1,519.76 cubic millimeters. What is the radius of this cone? Use pi = 3.14 and round your answer to the nearest hundredth

Answer 1

The expression for the volume of cone is :

`\begin{gathered} \text{Volume of Cone =}(1)/(3)\Pi r^2h \\ \text{where r = radius, h =height} \end{gathered}`

Since from the given figure we have, height of cone h= 12 mm

and from the given data, volum is V = 1519.76 cubic milimeter.

Subtitute the values in the expression for the volume of cone and solve for radius r,

`\begin{gathered} V=(1)/(3)\Pi r^2h \\ 1519.76=(1)/(3)\Pi r^2(12) \\ \text{ since, }\Pi=3.14 \\ (1519.76*3)/(\Pi(12))=r^2 \\ r^2=(4559.28)/(37.68) \\ r^2=121 \\ r=\sqrt[]{121} \\ r=11\text{ mm} \end{gathered}`

So, the radius of cone is 11 mm.

Answer : 11 mm