To solve this problem, we can use the Pythagorean Theorem. According to the information given, the diameter of the circle is 13 cm and the height of the cone is 6 cm.
Using the Pythagorean theorem, we have:
a^2 + b^2 = c^2
where a and b are the sides of the right triangle formed, and c is the hypotenuse (slant height in this case).
In this case, a is half of the diameter, which is 13/2 = 6.5 cm.
Plugging in the values, we have:
(6.5)^2 + (6)^2 = c^2
42.25 + 36 = c^2
78.25 = c^2
Taking the square root of both sides, we get:
c ≈ 8.8 cm
Therefore, the slant height must be approximately 8.8 cm.
Use the image to answer the question.
A drawing shows a circle showing diameter below a sector of a circle showing slant height. A double-headed arrow crossing the center of the circle is labeled as d equals diameter. A dotted double-headed arrow is drawn from the top point of the sector of the circle to a point along the curved edge. The arrow is labeled as lower L equals slant height.
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
11.5 cm
11.5 cm
14.3 cm
14.3 cm
8.8 cm
1 answer
1 answer