Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
Konery wants to make their waffle cones with a height of 6 in. Their current net design has a diameter of 2.5 in. and a slant h...Question
Konery wants to make their waffle cones with a height of 6 in. Their current net design has a diameter of 2.5 in. and a slant height of 6.25 in. Will this work for the desired height? Round the answer to the nearest tenth.(1 point
Answers
Answer
these are my only choices
No; the height is too long by 0.1 in.
No; the height is too long by 0.1 in.
No; the height is too long by 0.4 in.
No; the height is too long by 0.4 in.
No; the height is too long by 0.7 in.
No; the height is too long by 0.7 in.
No; the height is too short by 0.3 in.
No; the height is too long by 0.1 in.
No; the height is too long by 0.1 in.
No; the height is too long by 0.4 in.
No; the height is too long by 0.4 in.
No; the height is too long by 0.7 in.
No; the height is too long by 0.7 in.
No; the height is too short by 0.3 in.
Answer
could you show me the steps
Answered by
GPT 3.5
Yes, the current net design will work for the desired height of 6 in.
Explanation: The slant height of the cone is the hypotenuse of a right triangle with height and radius as the other two sides. Using the Pythagorean theorem, we can calculate the height:
height = sqrt(6.25^2 - 1.25^2) = sqrt(39.0625 - 1.5625) = sqrt(37.5) ≈ 6.1 in
Since the calculated height is greater than the desired height, the current net design will work for a height of 6 in.
Explanation: The slant height of the cone is the hypotenuse of a right triangle with height and radius as the other two sides. Using the Pythagorean theorem, we can calculate the height:
height = sqrt(6.25^2 - 1.25^2) = sqrt(39.0625 - 1.5625) = sqrt(37.5) ≈ 6.1 in
Since the calculated height is greater than the desired height, the current net design will work for a height of 6 in.
Answered by
GPT 3.5
No; the height is too long by 0.1 in.
Answered by
GPT 3.5
Sure!
Given:
Diameter (d) = 2.5 inches
Slant height (l) = 6.25 inches
Desired height (h) = 6 inches
To find the actual height of the cone, we can use the Pythagorean theorem, which states that:
l^2 = r^2 + h^2
Where:
l = Slant height
r = Radius (half of the diameter)
h = Height
Given in the problem:
l = 6.25 inches
d = 2.5 inches, so r = 1.25 inches
Substitute the values into the equation:
6.25^2 = 1.25^2 + h^2
39.0625 = 1.5625 + h^2
37.5 = h^2
h = √37.5 ≈ 6.1237 inches
Comparing this to the desired height:
Desired height = 6 inches
Actual height ≈ 6.1237 inches
The actual height is longer than the desired height by:
6.1237 - 6 ≈ 0.1 inches
Therefore, the correct answer is: No; the height is too long by 0.1 in.
Given:
Diameter (d) = 2.5 inches
Slant height (l) = 6.25 inches
Desired height (h) = 6 inches
To find the actual height of the cone, we can use the Pythagorean theorem, which states that:
l^2 = r^2 + h^2
Where:
l = Slant height
r = Radius (half of the diameter)
h = Height
Given in the problem:
l = 6.25 inches
d = 2.5 inches, so r = 1.25 inches
Substitute the values into the equation:
6.25^2 = 1.25^2 + h^2
39.0625 = 1.5625 + h^2
37.5 = h^2
h = √37.5 ≈ 6.1237 inches
Comparing this to the desired height:
Desired height = 6 inches
Actual height ≈ 6.1237 inches
The actual height is longer than the desired height by:
6.1237 - 6 ≈ 0.1 inches
Therefore, the correct answer is: No; the height is too long by 0.1 in.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.