Cylinders and Cones Practice
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Question
Use the image to answer the question.
A cone is marked with a height of 6 centimeters and a diameter of 2 centimeters, both shown as perpendicular dotted lines. The slant height is marked as 4 centimeters.
What is the length of the cone?
(1 point)
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wrong
Apologies for the incorrect answer. Let's try solving the problem correctly.
In a right triangle, the slant height (hypotenuse) is related to the height and radius (which is half the diameter) of the cone. We can use the Pythagorean theorem to find the length of the cone.
The height is given as 6 centimeters. The radius is half the diameter, so it is 2/2 = 1 centimeter.
We can create a right triangle with the height, radius, and slant height as its sides.
Using the Pythagorean theorem:
slant height^2 = height^2 + radius^2
4^2 = 6^2 + 1^2
16 = 36 + 1
16 = 37
This is not possible, as the square of a number cannot be less than the sum of the squares of other numbers.
There appears to be an error in the given information or the image. Without the correct values, we cannot accurately determine the length of the cone.
A cone is marked with a height of 6 centimeters and a diameter of 2 centimeters, both shown as perpendicular dotted lines. The slant height is marked as 4 centimeters.
Apologies for the confusion earlier.
In a cone, the slant height, height, and radius (which is half the diameter) are related.
The height of the cone is given as 6 centimeters.
The diameter of the cone is 2 centimeters, so the radius is 1 centimeter.
We can create a right triangle with the height, radius, and slant height as its sides.
Using the Pythagorean theorem:
slant height^2 = height^2 + radius^2
4^2 = 6^2 + 1^2
16 = 36 + 1
16 = 37
This is not possible, as the square of a number cannot be less than the sum of the squares of other numbers.
There appears to be an error in the given information or the image. Without the correct values, we cannot accurately determine the length of the cone.
To find the length of the cone, we need to use the Pythagorean theorem. The slant height of the cone, which is marked as 4 centimeters, represents the hypotenuse of a right triangle formed by the height, the radius, and the slant height.
The height is given as 6 centimeters, and the radius is half of the diameter, which is 1 centimeter. We can use the Pythagorean theorem to find the length of the cone:
length of cone = √(height^2 + radius^2)
Substituting in the given values:
length of cone = √(6^2 + 1^2)
length of cone = √(36 + 1)
length of cone = √37
length of cone ≈ 6.08 centimeters
So, the length of the cone is approximately 6.08 centimeters.
To find the length of the cone, we need to 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 and radius of the base are the other two sides of the right triangle.
Let's use the Pythagorean theorem to find the length of the cone:
c^2 = a^2 + b^2
c^2 = 6^2 + 2^2
c^2 = 36 + 4
c^2 = 40
Taking the square root of both sides:
c = √40
c ≈ 6.32
So, the length of the cone is approximately 6.32 centimeters.