Question

the figure gives the dimensions, in inches (in), of a typical safety cone. what is the length of the slant height s, in in? (round your answer to the nearest tenth of an inch.) do 4 problems

Explanation:

Step1: Identify radius and height

The radius $r$ of the base of the cone is half of the diameter. Given diameter is 12 in, so $r = \frac{12}{2}=6$ in, and the height $h = 28$ in.

Step2: Apply Pythagorean theorem for cone

The slant - height $s$ of a cone is given by the formula $s=\sqrt{r^{2}+h^{2}}$. Substitute $r = 6$ and $h = 28$ into the formula: $s=\sqrt{6^{2}+28^{2}}=\sqrt{36 + 784}=\sqrt{820}$.

Step3: Calculate and round

$\sqrt{820}\approx28.6$ in.

Answer:

28.6 in