Use the image to answer the question.
A cone is marked with a height of 12 centimeters and a diameter of 11 centimeters, both shown as perpendicular dotted lines. The slant height is 9 centimeters.
What is the height of the right circular cone?
(1 point)
Responses
9 cm
9 cm
11 cm
11 cm
12 cm
12 cm
5.5 cm
5.5 cm
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We can use the Pythagorean theorem to find the height of the right circular cone. The slant height, height, and radius of the cone form a right triangle.
The slant height is 9 centimeters, and the radius is half the diameter, so it is 11/2 = 5.5 centimeters.
Using the Pythagorean theorem, we have:
(height)^2 + (radius)^2 = (slant height)^2
(height)^2 + (5.5)^2 = (9)^2
(height)^2 + 30.25 = 81
(height)^2 = 81 - 30.25
(height)^2 = 50.75
height = sqrt(50.75)
height ≈ 7.12 cm
So, the height of the right circular cone is approximately 7.12 centimeters.