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)
a.8.8 cm
b.11.5 cm
c.14.3 cm
d.2.5 cm
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, the height of the cone is one side of the right triangle, the slant height is the hypotenuse, and the radius (half the diameter) is the other side.
Let's call the slant height "s", the height "h", and the radius "r". We are given that the height is 6 cm and the diameter is 13 cm, which means the radius is half of that or 6.5 cm.
Using the Pythagorean theorem, we can set up the equation:
s^2 = r^2 + h^2
s^2 = 6.5^2 + 6^2
s^2 = 42.25 + 36
s^2 = 78.25
To find the slant height, we take the square root of both sides:
s = √78.25
s ≈ 8.8
Therefore, the slant height must be approximately 8.8 cm.
The correct answer is a. 8.8 cm.