To find the slant height of the cone, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the height of the cone is one of the sides, the radius (half the diameter) of the base is the other side, and the slant height is the hypotenuse.
Using the Pythagorean Theorem equation, we have:
slant height^2 = height^2 + radius^2
plugging in the given values, we get:
slant height^2 = 6^2 + (13/2)^2
slant height^2 = 36 + 169/4
slant height^2 = 144/4 + 169/4
slant height^2 = 313/4
Now, we can solve this equation for the slant height:
slant height = sqrt(313/4)
slant height ≈ sqrt(78.25)
slant height ≈ 8.8 cm
Therefore, the slant height of the cone should be approximately 8.8 cm.
Chem Tech makes paper cones used to filter liquids in lab experiments. To make the paper cones, the company starts with the net of the shape, where the slant height is needed. The company wants the height of the cones to be 6 cm. If they make the diameter 13 cm, what must the slant height be? Use the Pythagorean Theorem and round the answer to the nearest tenth.
2 answers
A circus tent is in the shape of a square pyramid. Each edge of the square base is 20 m and its slant height is 13.5 m. Find the height of the tent. Round the answer to the nearest tenth.(1 point)