1. It is known that the volume of the pyramid V is equal to 1/3 of the product of the area S of the base by the height h.
2. According to the condition of the problem, it is given: at the base there is a rectangle with sides 6 cm and 8 cm, side edges L are 13 cm long.
The height h of the pyramid is lowered to the point of intersection of the diagonals d of the rectangle, its value is calculated by the Pythagorean theorem:
h² = L² – (1/2 d) ², whence h = √13² – 1/4 d².
D is determined from a right-angled triangle with legs 6 cm and 8 cm:
d = √6² + 8² = √36 + 64 = √100 = 10 cm.
So h = √169 – 1/4 * 100 = √144 = 12 cm.
3. Let’s calculate the V pyramid:
V = 1/3 * 6 cm * 8 cm * 12 cm = 192 cm³.
Answer: The volume is 192 cm³.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.