To find the slant height of the 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, the height of the cone (6 cm) is one of the legs of the right triangle, and the radius (half the diameter) of the cone (13 cm/2 = 6.5 cm) is the other leg.
So, using the Pythagorean theorem, we have:
slant height^2 = height^2 + radius^2
slant height^2 = 6^2 + 6.5^2
slant height^2 = 36 + 42.25
slant height^2 = 78.25
To find the slant height, we take the square root of both sides:
slant height = sqrt(78.25) ≈ 8.8 cm
Therefore, the slant height of the cone must 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.
(1 point)
Responses
2.5 cm
2.5 cm
14.3 cm
14.3 cm
11.5 cm
11.5 cm
8.8 cm
1 answer