the lateral surface area of a cone is 558pi cm^2. The radius is 18cm. Find the slant height to the nearest tenth.
17.1
16.4
31.0
11.6
you know lateral area of cone = π r l, where both SA and r are known, l is the slant height
π(18)l = 558π
l = 558/18 = ....
31!
Thank You!!!
Well, I have to say, that's one "conical" question! Let me calculate it for you. The formula for the lateral surface area of a cone is given by A = πrℓ, where r is the radius and ℓ is the slant height.
We are given that the lateral surface area is 558π cm^2 and the radius is 18 cm. Let's plug those values into the formula:
558π = π(18)(ℓ)
Now let's cancel out π on both sides:
558 = 18ℓ
Dividing both sides by 18:
ℓ = 558/18
Calculating that gives us ℓ ≈ 31 cm (rounded to the nearest tenth).
So, the answer is 31.0 cm. Looks like we've got a "cone-clusive" winner!
To find the slant height of a cone, you can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (slant height in this case) is equal to the sum of the squares of the other two sides (radius and height).
Given that the lateral surface area of the cone is 558π cm^2 and the radius is 18 cm, we can use the formula for the lateral surface area of a cone:
Lateral surface area = πrl,
where r is the radius and l is the slant height.
Let's plug in the given values and solve for the slant height:
558π cm^2 = π * 18 cm * l
Canceling out π on both sides, we get:
558 cm^2 = 18 cm * l
Dividing both sides by 18 cm:
31 cm = l
Therefore, the slant height to the nearest tenth is 31.0 cm. So, the correct answer is option C: 31.0 cm.
To find the slant height of a cone, you can use the formula:
Slant height = √(radius^2 + height^2)
In this case, you are given the radius of the cone as 18 cm and the lateral surface area as 558π cm^2. To find the height, we need to use the formula for the lateral surface area of a cone, which is:
Lateral Surface Area = π * radius * slant height
Substituting the given values, we have:
558π = π * 18 * slant height
Dividing both sides of the equation by π, we get:
558 = 18 * slant height
Simplifying further, we have:
slant height = 558 / 18
slant height ≈ 31
Therefore, the slant height to the nearest tenth is 31.0 cm.