To find the slant height, we need to use the Pythagorean theorem.
In a right triangle, the square of the hypotenuse (slant height) is equal to the sum of the squares of the other two sides.
Let's call the slant height "s". We can form a right triangle with the slant height as the hypotenuse, the radius as one of the legs, and the height as the other leg.
So, the height of the cone (6 cm) is one of the legs of the triangle. The radius of the base (half of the diameter) is 13/2 = 6.5 cm.
Using the Pythagorean theorem:
s^2 = 6.5^2 + 6^2
s^2 = 42.25 + 36
s^2 = 78.25
Taking the square root of both sides to find "s":
s = √(78.25)
s ≈ 8.8 cm
Therefore, the slant height must be approximately 8.8 cm.
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)
O 8.8 cm
O 11.5 cm
O 2.5 cm
O 14.3 cm
1 answer
1 answer