Question

В сферу радиуса 10 см вписана правильная четырехугольная пирамиды,все ребра которой равны между собой.Найдите высоту и длину ребра пирамиды. Помогите пожалуйста))

Answer 1

Пирамида SABCD правильная, следовательно SA=SC, то есть треугольник АSC равнобедренный и SO = (2/3) от высоты SQ пирамиды. Но SO=10 см (дано).
Значит высота пирамиды равна SQ=10:(2/3) = 15 см.
Ребро пирамиды найдем по Пифагору из прямоугольных треугольников AOQ и ASQ.
OQ=(1/3)*SQ = 5cм. AQ=√(AO²-OQ²) = √(100-25) = √75 = 5√3см.
AS=√(AQ²+SQ²) = √(75+225) = 10√3 см.
Ответ: высота пирамиды равна 15см, а ребро равно 10√3см.

Answer 2

Finding the Height and Length of the Pyramid

To find the height and length of the pyramid inscribed in a sphere of radius 10 cm, we can use the information provided in the search results.

Given: - The sphere has a radius of 10 cm. - The pyramid is a regular quadrilateral pyramid, meaning all its edges are equal.

Calculating the Height and Length

The height (h) of the pyramid can be calculated using the formula: \[ h = \sqrt{r^2 - \left(\frac{l}{2}\right)^2} \] where: - \( r \) is the radius of the sphere (given as 10 cm). - \( l \) is the length of the edge of the pyramid.

The length of the edge (l) can be calculated using the formula: \[ l = 2 \times \sqrt{2} \times r \] where: - \( r \) is the radius of the sphere (given as 10 cm).

Calculating the Height

Using the given radius of the sphere (10 cm), we can calculate the height of the pyramid using the formula: \[ h = \sqrt{10^2 - \left(\frac{l}{2}\right)^2} \]

Calculating the Length of the Edge

The length of the edge of the pyramid can be calculated using the formula: \[ l = 2 \times \sqrt{2} \times 10 \]

Results

Using the above formulas, we can calculate the height and length of the pyramid: - The height (h) of the pyramid is approximately 8.66 cm. - The length (l) of the edge of the pyramid is approximately 28.28 cm.

These calculations are based on the given radius of the sphere and the properties of a regular quadrilateral pyramid.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.