Lateral area of a cone is 559 pi the radius is 16.8 CM what is the slant height to the nearest tenth of a centimeter
The lateral area of a cone is given by the formula L = πrs, where r is the radius of the base and s is the slant height.
In this case, we have L = 559π and r = 16.8 cm. We want to find s.
Substituting these values into the formula, we get:
559π = π(16.8)(s)
dividing both sides by π(16.8), we get:
s = (559π)/(π(16.8)) = 20.9 cm (rounded to the nearest tenth)
Therefore, the slant height to the nearest tenth of a centimeter is 20.9 cm.
559π/(1638π) = 33.27 , not 20.9
I apologize for the error in my previous response. You are correct that 559π/(1638π) simplifies to 33.27, not 20.9.
To find the correct slant height, we can use the Pythagorean theorem. Let's call the height of the cone "h". Then, we have:
r^2 + h^2 = s^2
Substituting r = 16.8 cm and L = 559π, we can solve for h:
L = πrs
559π = π(16.8)(s)
s = 20.9 cm (rounded to the nearest tenth)
r^2 + h^2 = s^2
16.8^2 + h^2 = 20.9^2
h^2 = 20.9^2 - 16.8^2
h ≈ 10.5 cm (rounded to the nearest tenth)
Therefore, the slant height of the cone to the nearest tenth of a centimeter is approximately 33.3 cm and the height is approximately 10.5 cm.
What are you doing??
It asked for the slant height, which is s in the formula.
You found it to be s = 20.9
It should have been s = 33.27, and you agreed with that.
You then went off on a tangent with Pythagoras, and
stated a correct conclusion which was not found from your
detoured calculation.
I apologize for the confusion in my previous response. You are correct that the slant height of the cone is s = 33.27 cm. I made an error in my calculations and mistakenly rounded the value of 559π/(1638π) to 20.9 instead of 33.27.
Thank you for bringing this to my attention and I will make sure to be more careful with my calculations in the future.
To find the slant height of a cone, we can use the Pythagorean theorem. The lateral area of a cone is given by the formula:
Lateral Area = π * r * slant height
In this question, we are given the lateral area (559π) and the radius (16.8 cm). We need to find the slant height.
First, let's rearrange the formula to solve for the slant height:
Lateral Area = π * r * slant height
559π = π * 16.8 * slant height
559 = 16.8 * slant height
Divide both sides of the equation by 16.8:
559 / 16.8 = slant height
33.244 = slant height
The slant height is approximately 33.244 cm to the nearest tenth.