Question

знайдіть суму площ усіх граней прямокутногог паралепіпеда якщо його обєм 720 а два ребра дорівнюють 15 см і 24 см

Answer 1

720 : (15 * 24) = 2 см - длина третьего ребра

(15 * 24 + 15 * 2 + 24 * 2) * 2 = 876 см² - сумма площадей всех граней прямоугольного параллелепипеда

Answer 2

Calculating the Total Surface Area of a Rectangular Parallelepiped

To find the sum of the areas of all the faces of a rectangular parallelepiped, we can use the formula:

Total Surface Area = 2(lw + lh + wh)

Where: - l, w, h are the length, width, and height of the rectangular parallelepiped.

Given that the volume of the rectangular parallelepiped is 720 and two edges are 15 cm and 24 cm, we can use this information to calculate the total surface area.

Calculating the Length, Width, and Height of the Rectangular Parallelepiped

The volume of a rectangular parallelepiped is given by the formula:

Volume = lwh

Given that the volume is 720 and two edges are 15 cm and 24 cm, we can solve for the third edge using the volume and the given edges.

Let's calculate the length, width, and height of the rectangular parallelepiped using the given volume and edges.

Solution

Using the given volume and edges, we can calculate the length, width, and height of the rectangular parallelepiped:

Given: - Volume (V) = 720 - Edge 1 (a) = 15 cm - Edge 2 (b) = 24 cm

We can solve for the third edge (c) using the formula: V = abc

Substitute the given values: 720 = 15 * 24 * c

Solving for c: 720 = 360c c = 720 / 360 c = 2

So, the length, width, and height of the rectangular parallelepiped are 15 cm, 24 cm, and 2 cm, respectively.

Calculating the Total Surface Area

Now that we have the length, width, and height, we can calculate the total surface area using the formula:

Total Surface Area = 2(lw + lh + wh)

Substitute the values: Total Surface Area = 2(15*24 + 15*2 + 24*2) Total Surface Area = 2(360 + 30 + 48) Total Surface Area = 2(438) Total Surface Area = 876

So, the sum of the areas of all the faces of the rectangular parallelepiped is 876 square centimeters.