Chem Tech makes paper cones used to filter 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 slant height be? Use the Pythagorean Theorem and round the answer to the nearest tenth.
(1 point)
O 8.8 cm
O 11.5 cm
O 2.5 cm
O 14.3 cm
To find the slant height, we need to use the Pythagorean theorem.
In a right triangle, the square of the hypotenuse (slant height) is equal to the sum of the squares of the other two sides.
Let's call the slant height "s". We can form a right triangle with the slant height as the hypotenuse, the radius as one of the legs, and the height as the other leg.
So, the height of the cone (6 cm) is one of the legs of the triangle. The radius of the base (half of the diameter) is 13/2 = 6.5 cm.
Using the Pythagorean theorem:
s^2 = 6.5^2 + 6^2
s^2 = 42.25 + 36
s^2 = 78.25
Taking the square root of both sides to find "s":
s = √(78.25)
s ≈ 8.8 cm
Therefore, the slant height must be approximately 8.8 cm.
To find the slant height of the paper cone, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, one of the sides is the radius of the cone, which is half of the diameter (13 cm/2 = 6.5 cm). The other side is the height of the cone, which is given as 6 cm.
Using the Pythagorean Theorem:
hypotenuse^2 = base^2 + height^2
slant height^2 = (6.5 cm)^2 + (6 cm)^2
slant height^2 = 42.25 cm^2 + 36 cm^2
slant height^2 = 78.25 cm^2
Now, we need to find the square root of 78.25 cm^2 to find the slant height:
slant height ≈ √(78.25 cm^2)
slant height ≈ 8.8 cm
Therefore, the slant height of the paper cone should be approximately 8.8 cm. So, the correct answer is:
O 8.8 cm
To solve this problem, we can use the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse.
In this case, we can consider the height of the cone as one leg of the right triangle, the radius of the cone (half the diameter) as the other leg, and the slant height as the hypotenuse.
Let's call the height of the cone h, the radius r, and the slant height s.
We are given that the height of the cone is 6 cm, and the diameter is 13 cm. Therefore, the radius would be half of the diameter, which is r = 13/2 = 6.5 cm.
Now, using the Pythagorean Theorem, we can set up the equation:
h^2 + r^2 = s^2
Substituting the values we know:
6^2 + 6.5^2 = s^2
36 + 42.25 = s^2
78.25 = s^2
To find the slant height, we take the square root of both sides:
s = sqrt(78.25)
Using a calculator, we find:
s ≈ 8.8 cm
Therefore, the slant height of the paper cone should be approximately 8.8 cm. Hence, the correct answer is:
O 8.8 cm.