use the image to answer the question
find the length of the height of the cone
the radius of the cone is 5^2 cm
the height is 13^2
a^2 + b^2 = c^2
find the length of the height of the cone.
To find the length of the height of the cone, we can use the Pythagorean theorem.
Given that the radius of the cone is 5^2 cm (25 cm) and the height is 13^2 cm (169 cm), we can apply the formula:
a^2 + b^2 = c^2
where a represents the radius, b represents the height, and c represents the slant height of the cone.
Substituting the given values into the equation, we have:
25^2 + b^2 = 169^2
625 + b^2 = 28561
b^2 = 27936
Taking the square root of both sides, we get:
b = √27936
b ≈ 167.19 cm
Therefore, the length of the height of the cone is approximately 167.19 cm.
your supposed to multiply the numbers by 2
Apologies for the confusion. To find the length of the height of the cone, we need to multiply the given values by 2, as the formula for the height of a cone typically represents the perpendicular distance from the apex to the base.
Given that the radius of the cone is (5^2)*2 = 10 cm and the height is (13^2)*2 = 338 cm, we can apply the Pythagorean theorem:
a^2 + b^2 = c^2
Substituting the given values into the equation, we have:
10^2 + b^2 = 338^2
100 + b^2 = 114244
b^2 = 114244 - 100
b^2 = 114144
Taking the square root of both sides, we get:
b ≈ √114144
b ≈ 337.84 cm
Therefore, the length of the height of the cone is approximately 337.84 cm.
your supposed to multiply the numbers by 2.
Apologies for the oversight. Let's recalculate using the corrected values:
Given that the radius of the cone is 5^2 cm (25 cm), we multiply it by 2 to get a radius of 25 * 2 = 50 cm. Similarly, the height is 13^2 cm (169 cm), which when multiplied by 2 gives a height of 169 * 2 = 338 cm.
Applying the Pythagorean theorem, we have:
a^2 + b^2 = c^2
Substituting the values, we get:
50^2 + b^2 = 338^2
2500 + b^2 = 114244
b^2 = 114244 - 2500
b^2 = 111744
Taking the square root of both sides, we find:
b ≈ √111744
b ≈ 334.49 cm
Therefore, the length of the height of the cone is approximately 334.49 cm.
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 (c) is equal to the sum of the squares of the lengths of the two other sides (a and b).
In this case, we are given the radius (a) and the height (b) of the cone, and we need to find the length of the height (c).
The Pythagorean theorem formula is: a^2 + b^2 = c^2.
Given that the radius of the cone is 5^2 cm, we can determine the length of the radius by finding the square root of 5^2:
radius (a) = 5 cm.
Given that the height of the cone is 13^2 cm, we can determine the length of the height by finding the square root of 13^2:
height (b) = 13 cm.
Now, we can substitute these values into the Pythagorean theorem formula:
a^2 + b^2 = c^2.
Substituting the values, we get:
(5 cm)^2 + (13 cm)^2 = c^2.
Calculating the values, we have:
25 cm^2 + 169 cm^2 = c^2.
Combining the terms, we get:
194 cm^2 = c^2.
To find c, we take the square root of both sides:
√(194 cm^2) = √(c^2).
√(194) cm = c.
Therefore, the length of the height of the cone is approximately √194 cm.