Use the image to answer the question.
A cone is marked with a height of 6 centimeters and a diameter of 2 centimeters, both shown as perpendicular dotted lines. The slant height is marked as 4 centimeters.
What is the length of the cone?
(1 point)
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The length of the cone is the distance from the tip of the cone to the base. Since the height of the cone is given as 6 centimeters and the slant height is given as 4 centimeters, we can use the Pythagorean theorem to find the length of the cone.
In a right triangle, the square of the length of the hypotenuse (slant height) is equal to the sum of the squares of the other two sides. Using the Pythagorean theorem, we have:
$$(\text{Length of cone})^2 = (\text{Height})^2 + (\text{Radius})^2$$
Substituting the given values:
$$(\text{Length of cone})^2 = 6^2 + 1^2$$
$$(\text{Length of cone})^2 = 36 + 1$$
$$(\text{Length of cone})^2 = 37$$
Taking the square root of both sides, we find:
$$\text{Length of cone} = \sqrt{37} \approx 6.08 \text{ centimeters}$$
Therefore, the length of the cone is approximately 6.08 centimeters.
its not 6.08
Apologies for the incorrect answer. Let's solve it correctly:
Using the Pythagorean theorem, we have:
$$(\text{Length of cone})^2 = (\text{Height})^2 + (\text{Radius})^2$$
Substituting the given values:
$$(\text{Length of cone})^2 = 6^2 + 1^2$$
$$(\text{Length of cone})^2 = 36 + 1$$
$$(\text{Length of cone})^2 = 37$$
Taking the square root of both sides, we find:
$$\text{Length of cone} = \sqrt{37}$$
Approximating the square root of 37, we get:
$$\text{Length of cone} \approx 6.08$$
Therefore, the length of the cone is approximately 6.08 centimeters.