Suppose you have a conical shaped tent that you will use for camping. You want to ring along a tarp to fully cover the lateral area in case of inclement weather. The tent is 13 feet across and stands 8 feet high. What is the lateral area that the tarp would cover?
Thank you!
drfe
what is it
To find the lateral area of the conical shaped tent, we need to calculate the surface area of the curved part of the tent excluding the base.
First, we need to find the slant height of the cone. The slant height is the distance from the tip of the cone to any point on the circumference of its base.
Using the Pythagorean theorem, we can find the slant height (l) using the radius (r) and height (h) of the cone:
l = √(r² + h²)
Given that the tent is 13 feet across, the radius is half of that, which is 6.5 feet. And the height of the tent is 8 feet.
l = √(6.5² + 8²)
l = √(42.25 + 64)
l = √(106.25)
l ≈ 10.31 feet
Now, we can calculate the lateral area (A) using the formula:
A = π * r * l
Substituting the values we have:
A = π * 6.5 * 10.31
A ≈ 201.63 square feet
Therefore, the tarp would cover approximately 201.63 square feet of the lateral area of the conical shaped tent.
Lateral SA of cone = πrs
where r is the radius of the base and s is the slant height
we know r = 6.5 and
s^2 = 6.5^2 + 8^2
find s , plug into the formula and you are done