Question

В прямом параллелепипеде стороны основания равны 3 см и 4 см, а угол между ними-60. Площадь боковой поверхности ровна 15√3 см². Найти объём параллелепипеда.

Answer 1

V=S основания *H;
Сначала найдем площадь основания. Так как в основании лежит параллелограмм,    Sоснования= a*b*sin60=3*4*sgrt3/2=6*sgrt3.
ости найдем высоту Из площади боковой поверхности найдем высоту.
P основания=2(3+4)=14
Sбоковое=Роснования *H;
H=Sбоковое :Pоснования;
H=15*sgrt3:14=15sgrt3/14;
V=6sgrt3*15sgrt3/14=6*15*3/14=135/7. если нигде с цифрами не накосячила, то должно быть так

Answer 2

Given Information:

We are given that the sides of the base of a parallelepiped are 3 cm and 4 cm, and the angle between them is 60 degrees. The lateral surface area of the parallelepiped is 15√3 cm². We need to find the volume of the parallelepiped.

Solution:

To find the volume of the parallelepiped, we can use the formula:

Volume = Base Area × Height

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

Base Area = (1/2) × a × b × sin(θ)

where a and b are the lengths of the sides of the base, and θ is the angle between them.

Let's calculate the base area first:

Base Area = (1/2) × 3 cm × 4 cm × sin(60°)

Using the formula for the area of a triangle, we can calculate the base area:

Base Area = (1/2) × 3 cm × 4 cm × √3/2

Simplifying the expression, we get:

Base Area = 6√3 cm²

Now, we need to find the height of the parallelepiped. The lateral surface area of the parallelepiped is given as 15√3 cm². The lateral surface area can be calculated using the formula:

Lateral Surface Area = Perimeter of Base × Height

Since the parallelepiped has a rectangular base, the perimeter of the base is given by:

Perimeter of Base = 2 × (Length + Width)

In this case, the length and width of the base are 3 cm and 4 cm, respectively. Therefore:

Perimeter of Base = 2 × (3 cm + 4 cm) = 14 cm

Now, we can calculate the height of the parallelepiped:

Height = Lateral Surface Area / Perimeter of Base

Substituting the given values, we get:

Height = 15√3 cm² / 14 cm

Simplifying the expression, we get:

Height = (15/14)√3 cm

Finally, we can calculate the volume of the parallelepiped:

Volume = Base Area × Height

Substituting the values we calculated earlier, we get:

Volume = 6√3 cm² × (15/14)√3 cm

Simplifying the expression, we get:

Volume = 90/14 cm³

Therefore, the volume of the parallelepiped is 90/14 cm³.

Answer:

The volume of the parallelepiped is 90/14 cm³.