Chem Tech makes paper cones used to fitter liquids in lab experiments. To make the paper cones, the company starts with the net of the shape where the slant height is needed. The company wants the height of the cones to be 6 cm if they make the diameter 13 cm what must the sant height be? Use the Pythagorean Theorem and round the answer to the nearest tenth
(1 point)
Osson
O 25 an
O 1430m
To find the slant height of the cone, we can use the Pythagorean theorem.
The Pythagorean theorem states that the square of the hypotenuse (in this case, the slant height of the cone) is equal to the sum of the squares of the other two sides.
In this case, we have a right triangle with one side measuring 6 cm (the height of the cone) and another side measuring half of the diameter, which is 13/2 = 6.5 cm. Let's call the slant height "x".
Using the Pythagorean theorem:
x^2 = 6^2 + 6.5^2
x^2 = 36 + 42.25
x^2 = 78.25
Taking the square root of both sides:
x ≈ √78.25
x ≈ 8.8 cm
So, the slant height of the cone should be approximately 8.8 cm.
To find the slant height of the cone, we can use the Pythagorean Theorem. This theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the slant height of the cone represents the hypotenuse, the height represents one of the other sides, and the radius represents the other side. To find the slant height, we can set up the equation as follows:
height^2 + radius^2 = slant height^2
We are given that the height is 6 cm and the diameter is 13 cm. The radius can be calculated by dividing the diameter by 2:
radius = diameter / 2 = 13 cm / 2 = 6.5 cm
Substituting the known values into the equation, we get:
6^2 + 6.5^2 = slant height^2
36 + 42.25 = slant height^2
78.25 = slant height^2
To find the slant height, we need to take the square root of both sides:
slant height = sqrt(78.25)
Using a calculator, we can find that the square root of 78.25 is approximately 8.85.
Therefore, the slant height of the cone should be rounded to the nearest tenth, which is 8.9 cm.
To solve this problem, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can consider the height of the cone as one of the legs of a right triangle, the slant height as the hypotenuse, and the radius (half the diameter) as the other leg of the triangle.
Let's denote the height of the cone as h and the radius as r.
We are given that the height of the cone (h) should be 6 cm and the diameter (2r) is 13 cm.
Since the diameter is 13 cm, the radius is half of that, which is 13/2 = 6.5 cm.
Let's use the Pythagorean Theorem to solve for the slant height (l):
l^2 = h^2 + r^2
l^2 = 6^2 + 6.5^2
l^2 = 36 + 42.25
l^2 = 78.25
Taking the square root of both sides, we get:
l = √78.25
l ≈ 8.8 cm (rounded to the nearest tenth)
Therefore, the slant height should be approximately 8.8 cm.