Triangles Online Practice

Question

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14 of 1514 of 15 Items

Question
Use the image to answer the question.

An illustration shows a cylinder resting on its bottom base. The top base is visible. The part of the bottom base that is not visible is indicated by a dashed line. Parts of the cylinder are labeled. A large black point is shown in the center of the top face of the cylinder. A solid line extends from that point to the edge of the cylinder and is labeled r indicating the radius. The vertical line on the right side of the cylinder is labeled h. On the interior of the cylinder, a dotted line extends diagonally from top right to bottom left from where the radius line meets the edge down to the opposite side of the cylinder where the other face meets the edge. This line is labeled d.

Find the height, h
, of the cylinder. The radius, r
, is 5 cm and the diagonal, d
, is 15 cm. Round the answer to the nearest tenth.

(1 point)
Responses

11.2 cm
11.2 cm

18.0 cm
18.0 cm

14.1 cm
14.1 cm

15.8 cm

Answer 1

To find the height $h$ of the cylinder using the given radius $r$ and diagonal $d$, we can use the Pythagorean theorem. In this case, the radius forms one leg of a right triangle, the height $h$ is the other leg, and the diagonal $d$ is the hypotenuse.

According to the Pythagorean theorem: $$d^2=r^2+h^2$$

Here, we have:

• $r=5$ cm
• $d=15$ cm

Substituting these values into the equation, we get: $${15}^2=5^2+h^2$$ $$225=25+h^2$$ $$225-25=h^2$$ $$200=h^2$$ $$h=\sqrt{200}$$ $$h\approx 14.14$$

Rounding $h$ to the nearest tenth gives us: $$h\approx 14.1\text{ cm}$$

Thus, the answer is:

14.1 cm