Question

1)Из вершины В квадрата АВСD со стороной 6 см к его плоскости проведен перпендикуляр ВК. Найти объем пирамиды АВСDК, если АК=10 см.

Answer 1

$V= \frac{1}{3} S*h$

где S=6*6=36 см². Значит

$V= \frac{1}{3} 36*h$

V=12*h см³.

Где h- высота пирамиды.

Из треугольника АВК, где ∠АВК=90⁰ получаем ВК⊥(АВСD) по условию, а значит h=ВК.

АК²=АВ²+ВК²
10²=6²+ВК²
100=36+ВК²
ВК²=100-36
ВК²=64
ВК²=8²
ВК=8 см. 

V=12*8 см³.

V=96 см³.

Ответ: V=96 см³.

Answer 2

Calculation of the Volume of Pyramid ABCDK

To find the volume of the pyramid ABCDK, we need to know the base area and the height of the pyramid.

Given: - Side length of the square ABCD = 6 cm - Length of AK = 10 cm

To find the base area of the pyramid, we need to calculate the area of the square ABCD. Since all sides of a square are equal, the area can be calculated by squaring the length of one side.

Area of square ABCD = (side length)^2 = 6^2 = 36 square cm.

Now, to find the height of the pyramid, we can use the Pythagorean theorem. In triangle ABK, AB is the hypotenuse, AK is one side, and BK is the other side. We can calculate BK using the Pythagorean theorem:

BK = sqrt(AB^2 - AK^2) = sqrt(6^2 - 10^2) = sqrt(36 - 100) = sqrt(-64).

However, the square root of a negative number is not a real number, which means the given measurements do not form a valid pyramid. Please double-check the given measurements and ensure they are correct.

If you have any further questions, feel free to ask!