Chem tech makes paper cones used to filter liquids in lab experiments. To make the paper cones, the company starts with the net of the shape, where the slant height is needed. The company wants the height of the cones to be 6cm
To make the paper cones used to filter liquids in lab experiments, Chem tech starts with the net of the shape. The slant height of the cones is needed, and the company wants the height of the cones to be 6cm. The net of the cone is a 2-dimensional representation of the shape of the cone when it is unrolled and laid flat.
To find the slant height of the cone, we need to consider the properties of a cone. The slant height is the distance from the top of the cone to any point on the circumference of the base, and it can be found using the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In the case of a cone, the slant height (h) is the hypotenuse, and the height of the cone (6cm) is one of the other two sides. Let's call the radius of the base of the cone r.
Using the Pythagorean theorem, we can set up the equation:
h^2 = r^2 + 6^2
Since we want to find the slant height (h), we rearrange the equation:
h = √(r^2 + 36)
Therefore, to determine the slant height of the cone, Chem tech needs to know the radius of the base (r) and then calculate h using the formula h = √(r^2 + 36).