Question

В прямом параллелепипеде стороны основания равны 6 и 8см, а угол между ними 30градусов. площадь боковой поверхности равна 140 см2. найдите объем параллелепипеда

Answer 1

V=S(осн)*h
S(осн)=6*8*sin30=48*1/2=24(см²)
S(бок)=P*h=2(6+8)*h=2*14*h=28h(см²)
S(бок)=140 см² ( по условию)
28h=140
h=140:28
h=5см - высота параллелепипеда
V= 24*5= 120 (см³) - объём параллелепипеда

Answer 2

Given Information:

We are given the following information about a rectangular parallelepiped: - The lengths of the base sides are 6 cm and 8 cm. - The angle between the base sides is 30 degrees. - The lateral surface area is 140 cm².

Calculating the Volume:

To find the volume of the parallelepiped, we can use the formula: Volume = Base Area × Height.

The base area can be calculated using the lengths of the base sides and the angle between them. We can use trigonometry to find the height of the parallelepiped.

Let's calculate the base area first: - The base area is equal to the product of the lengths of the base sides: Base Area = 6 cm × 8 cm = 48 cm².

Next, we need to find the height of the parallelepiped. We can use the formula: Height = Base Side × sin(Angle).

Substituting the values, we get: - Height = 6 cm × sin(30 degrees) = 6 cm × 0.5 = 3 cm.

Now, we can calculate the volume: - Volume = Base Area × Height = 48 cm² × 3 cm = 144 cm³.

Therefore, the volume of the parallelepiped is 144 cm³.

Conclusion:

The volume of the given rectangular parallelepiped with base sides of 6 cm and 8 cm, an angle of 30 degrees between them, and a lateral surface area of 140 cm² is 144 cm³.