Question

В прямом параллелепипеде стороны основания 4 см и 5 см, образуют угол 30 °. Боковая поверхность 49 см в квадрате. Найти V параллелепипеда.

Answer 1

В основании параллелепипеда параллелограмм.Площадь параллелограмма равна:
Sabcd= 4 * 5 * Sin30° = 20 * 1/2 = 10 см²
Площадь боковой поверхности переллелепипеда равна:
Sбок = Pосн * H        Pосн = 2(4 + 5) = 18 см
H = Sбок : Pосн = 49 : 18 = 49/18 см
Объём прямого параллелепипеда равен:
V = Sосн * H = 10 * 49/18 = 245/9 = 27 2/9 см³

Answer 2

Calculating the Volume of a Parallelepiped

To calculate the volume of a parallelepiped, we can use the formula:

V = A * h

Where: - V is the volume of the parallelepiped - A is the area of the base - h is the height of the parallelepiped

Given Information

The sides of the base of the parallelepiped are 4 cm and 5 cm, and they form a 30° angle. The lateral surface area is 49 cm².

Calculating the Area of the Base

To find the area of the base, we can use the formula for the area of a parallelogram:

A = a * b * sin(θ)

Where: - a and b are the lengths of the sides of the parallelogram - θ is the angle between the sides

Given that the sides of the base are 4 cm and 5 cm, and they form a 30° angle, we can calculate the area of the base.

A = 4 * 5 * sin(30°)

Using the trigonometric identity sin(30°) = 1/2, we get:

A = 4 * 5 * (1/2) = 10 cm²

Calculating the Volume

Now that we have the area of the base, we can calculate the volume using the formula V = A * h. However, the height of the parallelepiped is not provided in the given information.

Conclusion

To calculate the volume of the parallelepiped, we need the height of the parallelepiped. If the height is provided, we can use the formula V = A * h to find the volume.