Question

what is the length of the side of the cone? 1.75 cm 12 cm

Explanation:

Step1: Identify the formula for the slant height of a cone

The slant height \( l \) of a cone can be found using the Pythagorean theorem, where \( l = \sqrt{r^2 + h^2} \), with \( r \) being the radius of the base and \( h \) being the height of the cone.

Step2: Find the radius of the base

The diameter of the base is given as \( 12 \) cm, so the radius \( r = \frac{12}{2} = 6 \) cm. The height \( h = 1.75 \) cm.

Step3: Calculate the slant height

Substitute \( r = 6 \) cm and \( h = 1.75 \) cm into the formula:
\[
l = \sqrt{6^2 + 1.75^2} = \sqrt{36 + 3.0625} = \sqrt{39.0625} = 6.25
\]

Answer:

\( 6.25 \)