From a rectangular parallelepiped, the base of which is a square with a side of 4 cm, a cube with an edge of 3 cm was cut off.

| June 26, 2021 | education

From a rectangular parallelepiped, the base of which is a square with a side of 4 cm, a cube with an edge of 3 cm was cut off. What is the volume of the resulting figure if the height of the parallelepiped is 7 cm?

The volume (Vp) of a rectangular parallelepiped is equal to the product of the area of ​​the base (S) by the height of the parallelepiped (H), that is, Vp = S * H. Since the base of a rectangular parallelepiped is a square, then using the formula for determining the area (S) of a square S = a ^ 2 (where a is the side of the square), we can obtain the following formula for determining the volume of a rectangular parallelepiped: Vn = a ^ 2 * H.
Therefore, Vp = (4 cm) ^ 2 * (7 cm) = (4 * 4 * 7) cm3 = 112 cm3.
Recall the formula for calculating the volume of a cube (Vk) along the known edge a. It has the form: Vk = a ^ 3. According to this formula, the volume of a cut cube with an edge of 3 cm is Vк = (3 cm) ^ 3 = (3 * 3 * 3) cm3 = 27 cm3.
Let us subtract the volume of the cube Vk from the volume of the rectangular parallelepiped Vp. Then we have: Vp – Vk = 112 cm2 – 27 cm3 = (112 – 27) cm3 = 85 cm3.
Answer: 85 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.