Question

surface area and volume of three-dimensional fi...
cylinders and cones
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what is the length of the cone?
(1 point)

Explanation:

Step1: Identify given values

Height $h=6$ cm, radius $r=2$ cm

Step2: Apply Pythagorean theorem

The slant length $l$ of the cone is calculated using $l=\sqrt{r^2+h^2}$
$$l=\sqrt{2^2+6^2}=\sqrt{4+36}=\sqrt{40}=2\sqrt{10}\approx6.32$$
Wait, correct the misread: The diagram labels the slant side as 4 cm? No, the question asks for the length (slant height). Recheck: The cone's height is 6 cm, radius 2 cm.

Step1: Confirm target measurement

We need the slant height $l$.

Step2: Use cone slant height formula

$$l=\sqrt{r^2+h^2}$$
Substitute $r=2$ cm, $h=6$ cm:
$$l=\sqrt{2^2 + 6^2}=\sqrt{4+36}=\sqrt{40}=2\sqrt{10}\approx6.32$$
Wait, no—wait the diagram has a 4 cm label on the side, but that must be a misread. Wait the question asks "length of the cone" which refers to slant height. The given height is 6 cm, radius 2 cm.

Answer:

$2\sqrt{10}$ cm (or approximately 6.32 cm)