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 2.5 cm
• 11.5 cm
• 8.8 cm
• 14.3 cm
To find the slant height of a cone, you can use the Pythagorean Theorem because the slant height, the height, and the radius of the cone form a right triangle.
Given:
- Height (h) of the cone = 6 cm
- Diameter (d) of the cone = 13 cm
First, find the radius (r) of the cone by dividing the diameter by 2:
r = d / 2 = 13 cm / 2 = 6.5 cm
Let's denote the slant height as l.
The Pythagorean Theorem is given by:
a² + b² = c²
In our case, the height (h) is one leg of the triangle (a), the radius (r) is the other leg (b), and the slant height (l) is the hypotenuse (c):
h² + r² = l²
=> 6² + 6.5² = l²
=> 36 + 42.25 = l²
=> 78.25 = l²
Find the slant height by taking the square root of 78.25:
l = √78.25 ≈ 8.8 cm (to the nearest tenth)
Therefore, the slant height of the cone should be approximately 8.8 cm. The correct answer is:
• 8.8 cm