Use the image to answer the question.
An illustration shows a cone that rests flat on the circular base. The visible circumference of the base and sides are in solid lines. The circumference of the base at the back that is not visible is indicated by a dashed line. Parts are labeled. A large point is marked in the center of the base. A solid line passes through this point and extends from one edge of the base to the other to indicate the diameter of the base. The line is labeled d equals 10 centimeters. The right side of the cone extending from where the diameter meets the edge of the base up to the point of the cone shows a slant height of 13 centimeters. A dotted line extends from the interior of the vertex of the cone down to the point marked in the center of the base. A right angle is indicated where the dotted height line meets the diameter line in the center of the base.
Find the length of the height of the cone.
(1 point)
cm
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Unfortunately, since I cannot see the image you are referring to, I cannot answer the question. Could you please provide a description of the image or the necessary information for me to calculate the length of the height of the cone?
To find the length of the height of the cone, we can use the Pythagorean Theorem.
In the given image, the slant height of the cone is 13 centimeters, and the diameter of the base is 10 centimeters.
The slant height (l) represents the hypotenuse of a right triangle, while the radius (r) and height (h) represent the other two sides.
Using the Pythagorean Theorem, we can write:
l^2 = r^2 + h^2
Substituting the given values, we have:
13^2 = (5)^2 + h^2
169 = 25 + h^2
Simplifying, we get:
h^2 = 169 - 25
h^2 = 144
Taking the square root of both sides, we find:
h = 12 centimeters
Therefore, the length of the height of the cone is 12 centimeters.
To find the length of the height of the cone, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the slant height of the cone is the hypotenuse, and the height of the cone is one of the other two sides.
In the given image, we can see that the slant height is 13 centimeters and the diameter of the base is 10 centimeters. To find the height, we need to find the length of the missing side in the right triangle formed by the diameter, height, and slant height.
Using the Pythagorean theorem, we can set up the equation:
(height)^2 + (radius)^2 = (slant height)^2
Since the radius is half the diameter, it is equal to 10/2 = 5 centimeters.
Substituting the values we have:
(height)^2 + (5 cm)^2 = (13 cm)^2
Simplifying the equation:
(height)^2 + 25 cm^2 = 169 cm^2
Subtracting 25 cm^2 from both sides of the equation:
(height)^2 = 144 cm^2
Taking the square root of both sides to solve for the height:
height = √144 cm
height = 12 cm
Therefore, the length of the height of the cone is 12 centimeters.