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.

Question

(1 point)
• 2.5 cm
• 14.3 cm
8.8 cm
11.5 cm

Answer 1

To determine the slant height of the cone, we can use the Pythagorean Theorem.

The dimensions we have are:

• Height \( h = 6 \) cm
• Diameter = 13 cm
• Therefore, the radius \( r = \frac{13}{2} = 6.5 \) cm

According to the Pythagorean Theorem: \[ l^2 = r^2 + h^2 \] where:

• \( l \) is the slant height
• \( r \) is the radius of the base
• \( h \) is the height of the cone

Plugging in the values we have: \[ l^2 = (6.5)^2 + (6)^2 \] Calculating the squares: \[ l^2 = 42.25 + 36 \] \[ l^2 = 78.25 \]

Now, taking the square root: \[ l = \sqrt{78.25} \approx 8.83 \]

Rounding to the nearest tenth gives us: \[ l \approx 8.8 \text{ cm} \]

Thus, the slant height must be 8.8 cm.