To calculate the volume of a cone, we can use the following formula. In this formula r is the radius and h is the height of a cone.
V= 13Ï€ r^2 h
Let's start by finding the value of r.
We are given that the lateral area of a cone is 71.6 mm^2 and the slant height is 6mm. Let's substitute the values into the formula for the lateral area and solve the equation for r.
We found that the radius is approximately 3.8mm. We are also given that the slant height is 6 mm. Let's take a look at the diagram.
Now let's notice that a slant height, the radius, and the height h form a right triangle.
Next, we can calculate the height of the cone by the Pythagorean Theorem. Let's write an equation according to this theorem.
h^2+ 3.8^2= 6^2
Now let's solve above equation for h.
Note that, when solving the above equation, we only needed to consider the principal root because h is a positive number. Finally we have enough information to calculate the volume. Let's substitute 3.8 for r and 4.6 for h into the volume formula.
