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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

14.1 cm
14.1 cm

15.8 cm
15.8 cm

11.2 cm
11.2 cm

18.0 cm

Answer 1

To find the height \( h \) of the cylinder using the radius \( r \) and the diagonal \( d \), we can use the Pythagorean theorem. The diagonal \( d \) serves as the hypotenuse, while the height \( h \) and the radius \( r \) represent the two legs of a right triangle.

According to the Pythagorean theorem: \[ d^2 = r^2 + h^2 \]

Given:

• \( r = 5 \) cm
• \( d = 15 \) cm

Now we can substitute the values into the equation: \[ 15^2 = 5^2 + h^2 \]

Calculating the squares: \[ 225 = 25 + h^2 \]

Now, subtract 25 from both sides: \[ 225 - 25 = h^2 \] \[ 200 = h^2 \]

Next, take the square root of both sides to find \( h \): \[ h = \sqrt{200} \] \[ h \approx 14.14 \]

Rounding to the nearest tenth gives: \[ h \approx 14.1 \text{ cm} \]

Thus, the height \( h \) of the cylinder is 14.1 cm.