how many feet long is the radius of the cone. the height is 99ft and the slant is 101ft. what is the radius?
To find the radius of the cone, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the height of the cone is one side, the slant height is the hypotenuse, and the radius is the other side that we need to find.
Let's denote the radius of the cone as "r". According to the Pythagorean theorem, we have:
r^2 + 99^2 = 101^2
r^2 + 9801 = 10201
r^2 = 10201 - 9801
r^2 = 400
Taking the square root of both sides, we get:
r = √400 = 20
Therefore, the radius of the cone is 20 feet long.
To find the radius of a cone, we need the height and the slant height. The slant height is the distance from the tip of the cone to any point on its base.
In this case, the height is given as 99 ft and the slant height is given as 101 ft.
To find the radius, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides (in this case, the radius and the height).
Let's call the radius "r". Using the Pythagorean theorem, we have:
r^2 + 99^2 = 101^2
Simplifying this equation, we get:
r^2 + 9801 = 10201
Subtracting 9801 from both sides, we get:
r^2 = 400
Taking the square root of both sides, we get:
r = 20
Therefore, the radius of the cone is 20 ft.
To find the radius of a cone, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we can consider the height (99ft) as one side and the slant height (101ft) as the hypotenuse of a right triangle. The other side would represent the radius of the cone that we're trying to find.
Let's calculate it step-by-step:
Step 1: Use the Pythagorean theorem to find the other side (radius).
- 99^2 + b^2 = 101^2 (where b represents the radius)
- 9801 + b^2 = 10201
Step 2: Rearrange the equation to solve for b (the radius).
- b^2 = 10201 - 9801
- b^2 = 400
- b = √400 (taking the square root of both sides)
- b = 20
The radius of the cone is 20 feet.