hem 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 6 cm. If they make the diameter 13 cm, what must the slant height be? Use the pythagorean Theorem and round the answer to the nearest tenth
To find the slant height of the cone, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides.
In this case, the height of the cone is given as 6 cm, and the diameter is 13 cm (which means the radius is half of the diameter, or 6.5 cm).
Let's call the slant height "s". The height (h) and radius (r) form a right triangle, with the slant height as the hypotenuse.
Using the Pythagorean Theorem, the equation becomes:
s^2 = r^2 + h^2
Substituting the given values:
s^2 = 6.5^2 + 6^2
s^2 = 42.25 + 36
s^2 = 78.25
Taking the square root of both sides to solve for s:
s ≈ √78.25
s ≈ 8.8 cm
Therefore, the slant height of the cone should be approximately 8.8 cm.