Question

В основании прямой призмы лежит параллелограмм,один угол которого равен 150 градусов, а стороны равны 4 см и 10 см. Вычислите объем и площадь поверхности призмы,если ее высота равна 0,4 дм. ПОМОГИТЕ, ПРОШУУ!!

Answer 1

Объем призмы равен произведению площади основания и высоты. Площадь поверхности состоит из 2 площадей основания и боковой поверхности, которая равна периметру основания на высоту. Нужна площадь параллелограмма.
S= a*b* sin α = 4*10* sin 150° = 4*10*0.5 =20 см².
P = 2a+2b = 2*4+2*10 = 28 cм.
V= S*H = 20 * 4 = 80 см³( 0,4 дм = 4 см).
S(пов) = 2*S +P*H = 2*20 +28*4 = 152 см².

Answer 2

Calculation of Volume and Surface Area of a Prism

To calculate the volume and surface area of a prism, we need to know the dimensions of the base and the height of the prism. In this case, the base of the prism is a parallelogram with one angle measuring 150 degrees and sides measuring 4 cm and 10 cm. The height of the prism is given as 0.4 dm.

Let's calculate the volume and surface area step by step:

Calculating the Volume of the Prism

The volume of a prism can be calculated by multiplying the area of the base by the height of the prism. Since the base of the prism is a parallelogram, we can calculate its area using the formula: Area = base * height.

In this case, the base of the prism is a parallelogram with sides measuring 4 cm and 10 cm. To calculate the area of the base, we need to find the height of the parallelogram. Since one angle of the parallelogram is given as 150 degrees, we can use trigonometry to find the height.

Using the formula height = side * sin(angle), we can calculate the height of the parallelogram.

Let's calculate the height of the parallelogram first:

height = 4 cm * sin(150 degrees)

To calculate the sine of 150 degrees, we can use a calculator or refer to trigonometric tables. The sine of 150 degrees is 0.5.

height = 4 cm * 0.5 = 2 cm

Now that we have the height of the parallelogram, we can calculate the area of the base:

Area = base * height = 10 cm * 2 cm = 20 cm^2

Finally, we can calculate the volume of the prism:

Volume = Area * height = 20 cm^2 * 0.4 dm

Note that we need to convert the height from decimeters (dm) to centimeters (cm) to ensure consistent units. Since 1 dm is equal to 10 cm, the height in centimeters is 0.4 dm * 10 cm/dm = 4 cm.

Volume = 20 cm^2 * 4 cm = 80 cm^3

Therefore, the volume of the prism is 80 cubic centimeters (cm^3).

Calculating the Surface Area of the Prism

The surface area of a prism can be calculated by adding the areas of all its faces. In this case, the prism has two identical parallelogram faces and three rectangular faces.

To calculate the area of a parallelogram, we use the formula: Area = base * height. In this case, the base and height of the parallelogram are 10 cm and 2 cm, respectively.

Area of each parallelogram face = 10 cm * 2 cm = 20 cm^2

Since the prism has two identical parallelogram faces, the total area contributed by the parallelogram faces is:

Total area contributed by parallelogram faces = 2 * 20 cm^2 = 40 cm^2

To calculate the area of a rectangular face, we use the formula: Area = length * width. In this case, the length and width of the rectangular faces are 10 cm and 4 cm, respectively.

Area of each rectangular face = 10 cm * 4 cm = 40 cm^2

Since the prism has three rectangular faces, the total area contributed by the rectangular faces is:

Total area contributed by rectangular faces = 3 * 40 cm^2 = 120 cm^2

Finally, we can calculate the total surface area of the prism by adding the areas of all its faces:

Total surface area = Total area contributed by parallelogram faces + Total area contributed by rectangular faces

Total surface area = 40 cm^2 + 120 cm^2 = 160 cm^2

Therefore, the surface area of the prism is 160 square centimeters (cm^2).

To summarize: - The volume of the prism is 80 cubic centimeters (cm^3). - The surface area of the prism is 160 square centimeters (cm^2).

I hope this helps! Let me know if you have any further questions.