To find the slant height, we can use the Pythagorean theorem. The slant height, height, and radius (half of the diameter) form a right triangle.
Using the Pythagorean theorem, we have:
radius² + height² = slant height²
The radius is half of the diameter, so it is (1/2) * 13 = 6.5 cm.
Substituting the values, we have:
6.5² + 6² = slant height²
42.25 + 36 = slant height²
78.25 = slant height²
Taking the square root of both sides, we have:
slant height ≈ √78.25 ≈ 8.84 cm
Rounding this to the nearest tenth, the slant height should be approximately 8.8 cm.
Therefore, the correct answer is:
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
8.8 cm
8.8 cm
2.5 cm
2.5 cm
11.5 cm
11.5 cm
14.3 cm
1 answer