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steposvetlana [31]
2 years ago
7

Hi.

Mathematics
1 answer:
Volgvan2 years ago
7 0

Answer:  radius = 5.83 cm     height = 8.12 cm

<u>Step-by-step explanation:</u>

First, let's find the circumference of the 210° section of the circle.

C=2\pi r\bigg(\dfrac{\theta}{360^o}\bigg)\\\\\\C=2\pi(10)\bigg(\dfrac{210^o}{360^o}\bigg)\\\\\\C=\dfrac{35}{3}\pi

The circumference of the the cone is \dfrac{35}{3}\pi .  We can use this to find the radius .

C=2\pi r\\\\\dfrac{35}{3}\pi=2\pi r\\\\\\\dfrac{35\pi}{3\cdot 2\pi}=r\\\\\\\dfrac{35}{6}=r\\\\\\5.83=r

When you fold the 210° section into a cone, the slant height is the original radius of 10.  We can use the radius and slant height of the cone to form a right triangle with the height.  Use the Pythagorean Theorem to find the height.

radius² + height² = slant height²

\dfrac{35}{6}^2\  +\ h^2=10^2\\\\\\.\qquad \quad h^2=10^2-\bigg(\dfrac{35}{6}\bigg)^2\\\\.\qquad \quad h=\sqrt{\dfrac{6^2(10)^2-35^2}{6^2}}\\\\\\.\qquad \quad h=\sqrt{\dfrac{2375}{36}}\\\\\\.\qquad \quad h=8.12

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