How do you find the slant height of a cone with a height of 12.5 cm and a diameter of 7cm?
s^2 = h^2 + r^2
where r is the radius
Draw a side view to see why this is so.
I just need the answer cuz I promised I would have this done.
To find the slant height of a cone, you can use the Pythagorean theorem. The slant height is the distance from the tip of the cone to any point on the base along the curved surface.
Step 1: Identify the known information:
- Height (h) = 12.5 cm
- Diameter (d) = 7 cm (Diameter is twice the radius, so the radius would be 7/2 = 3.5 cm)
Step 2: Find the slant height using the Pythagorean theorem:
The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides in a right triangle.
- The height (h) is the vertical side.
- The slant height (l) is the hypotenuse.
- Half of the diameter (d/2) is the base of the right triangle.
By applying the Pythagorean theorem, we get:
l^2 = h^2 + (d/2)^2
l^2 = 12.5^2 + (7/2)^2
l^2 = 156.25 + 12.25
l^2 = 168.5
l = √168.5
l ≈ 12.992 cm
Therefore, the slant height of the cone is approximately 12.992 cm.