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 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.
(1 point)
Responses
To calculate the slant height of the cone, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, one of the sides is the radius of the base of the cone, which is half of the diameter (13 cm / 2 = 6.5 cm). The other side is the height of the cone, which is given as 6 cm.
Let's label the slant height as "s". Using the Pythagorean theorem, we have:
s^2 = r^2 + h^2
s^2 = (6.5 cm)^2 + (6 cm)^2
s^2 = 42.25 cm^2 + 36 cm^2
s^2 = 78.25 cm^2
To find the slant height "s", we take the square root of both sides:
s = √78.25 cm^2
s ≈ 8.8 cm
Therefore, the slant height of the paper cone should be approximately 8.8 cm.