Question

slant height of a the base of 40 with the SA equaling2800

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the slant height of a cone with a base circumference of 40 units and a surface area of 2800 square units, we can use the following formula:

Surface Area of Cone = πr(r + l)

where r is the radius of the base and l is the slant height.

Given that the circumference of the base is 40 units, we can find the radius by using the formula:

Circumference = 2πr

40 = 2πr

Dividing both sides by 2π:

r = 40 / (2π)
r ≈ 6.37 units

Now, let's substitute the given surface area (2800) and the calculated radius (6.37) into the surface area formula:

2800 = π(6.37)(6.37 + l)

2800 = 40.22 + πl

Subtracting 40.22 from both sides:

2759.78 = πl

Dividing both sides by π:

l ≈ 876.59 units

Therefore, the slant height of the cone's base is approximately 876.59 units.