Question
An open cone has a slant height of 5 m and a cunved
surface area of
base.
surface area of
base.
Ask by Hanson Young. in Indonesia
Mar 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The radius of the circular base is approximately 15.98 meters.
Solution
It seems there was an error in the calculation. Let’s simplify the expression manually:
Divide both sides by 5:
Now, divide both sides by
Let’s calculate the value of
Calculate the value by following steps:
Calculate the value by following steps:
- step0: Calculate:
- step1: Remove the parentheses:
- step2: Multiply the numbers:
- step3: Convert the expressions:
- step4: Multiply by the reciprocal:
- step5: Multiply:
- step6: Multiply:
The radius of the circular base of the open cone is approximately 15.97917 m.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
To find the radius of the circular base of the cone, we can use the formula for the curved surface area (CSA) of a cone, which is given by:
where
Solving for
So, the radius of the circular base is approximately
Developing a keen understanding of geometry can illuminate the beauty in mathematics! Conical shapes are seen in everyday life, from traffic cones to party hats. Next time you attend a birthday party, take a moment to appreciate the shape and its geometric properties—you might spot some cones around you!
If you’re diving into calculations involving cones, remember to pay careful attention to the measurements you have, particularly ensuring you’re using the correct values for the area and height. A common mistake is mixing up slant height with the vertical height; these are distinct measurements. Keeping them straight will save you from frustrating errors on your path to mastering geometry!
