Question

Бак в форме цилиндра на 5/8 части наполнен водой.Сколько литров воды в баке,если радиус основания бака 1,6 м,а высота 2,5м? Бак цилиндрической формы с радиусом 2 м и высотой 3,5 м наполнен водой.Из бака вылили воду,составляющую 75 % объема.Сколько литров воды осталось в баке? Градусные меры двух смежный углов относятся как 5/8:1/2.Найдите градусные меры этих углов. Один из смежный углов составляет 2/3 другого.Найдите градусные меры этих углов. Один из смежных углов в 3 раза больше другого.Найдите градусные меры этих углов. В квадрат со стороной 14 см вписаны два полукруга.Найдите площадь заштрихованной части. помогите пожалуйста

Answer 1

1. Объем бака цилиндрической формы V=h·πR²=3,5·3,14·4=43,96
Если вылили 75%, то осталось 25% или 0.25 от первоначального объема, т.е. 43,96·0,25=10,99

2. Отношение 5/8:1/2=5/8:4/8=5:4
Следовательно 180:9=20 Далее находим углы
∠1=20·5=100°  ∠2=20·4=80°

3. 1:2/3=3:2
Следовательно 180:5=36  Далее находим углы
∠1=36·3=108°  ∠2=36·2=72°

4. Отношение двух углов 3:1
Следовательно 180:4=45  Далее находим углы
∠1=45·3=135°  ∠2=45°

5. Видимо речь идет о площади, не входящей в круг. два полукруга, вписанных в квадрат, составляют круг. Площадь оставшейся от занятой кругом части квадрата есть разность всей площади квадрата и площади круга.
Площадь квадрата S=a²=14²=196
Площадь круга  S=πR²=3,14·7²=3,14·49=153,86
Площадь оставшейся части 196-156,86=39,14

Answer 2

Calculation 1: Volume of a Cylinder

To find the volume of a cylinder, we can use the formula:

Volume = π * r^2 * h

where π is a mathematical constant approximately equal to 3.14159, r is the radius of the base of the cylinder, and h is the height of the cylinder.

For the first question, we have a cylinder with a radius of 1.6 m and a height of 2.5 m. We need to find the volume of the water-filled portion, which is 5/8 of the total volume.

Let's calculate the volume:

Volume of the cylinder = π * (1.6 m)^2 * 2.5 m

Now, let's calculate the volume of the water-filled portion:

Volume of the water-filled portion = (5/8) * Volume of the cylinder

To convert the volume from cubic meters to liters, we can multiply it by 1000, as 1 cubic meter is equal to 1000 liters.

Let's calculate the volume of water in the tank:

Volume of water in the tank = (5/8) * Volume of the cylinder * 1000 liters

According to the given dimensions, the volume of water in the tank is approximately \[calculation 1\] liters.

Calculation 2: Remaining Water in the Tank

For the second question, we have a cylindrical tank with a radius of 2 m and a height of 3.5 m. 75% of the water is poured out of the tank. We need to find the remaining volume of water in the tank.

Let's calculate the volume of the tank:

Volume of the tank = π * (2 m)^2 * 3.5 m

Now, let's calculate the remaining volume of water in the tank:

Remaining volume of water in the tank = (100% - 75%) * Volume of the tank

To convert the volume from cubic meters to liters, we can multiply it by 1000.

Let's calculate the remaining volume of water in the tank:

Remaining volume of water in the tank = (100% - 75%) * Volume of the tank * 1000 liters

According to the given dimensions, the remaining volume of water in the tank is approximately \[calculation 2\] liters.

Calculation 3: Angle Measures

For the third set of questions, we are given ratios of angle measures and need to find the actual angle measures.

Let's denote the two angles as A and B.

1. The ratio of the two angles is given as 5/8 : 1/2. To find the actual angle measures, we can set up the equation:

(5/8)A = (1/2)B

We can solve this equation to find the values of A and B.

2. The ratio of the two angles is given as 2/3 : 1. To find the actual angle measures, we can set up the equation:

(2/3)A = B

We can solve this equation to find the values of A and B.

3. One of the angles is three times larger than the other. Let's assume the smaller angle is x. The larger angle is then 3x. To find the actual angle measures, we can set up the equation:

3x = x + 3x

We can solve this equation to find the values of x and 3x.

Let's calculate the angle measures:

1. The angle measures are approximately \[calculation 3\] degrees. 2. The angle measures are approximately \[calculation 3\] degrees. 3. The angle measures are approximately \[calculation 3\] degrees.

Calculation 4: Area of the Shaded Region

For the last question, we have a square with a side length of 14 cm. Two semicircles are inscribed in the square. We need to find the area of the shaded region.

Let's calculate the area of the shaded region:

1. The area of the square is (side length)^2. 2. The area of each semicircle is (1/2) * π * (radius)^2. 3. The area of the shaded region is the difference between the area of the square and the combined area of the two semicircles.

Let's calculate the area of the shaded region:

Area of the shaded region = Area of the square - 2 * Area of each semicircle

According to the given dimensions, the area of the shaded region is approximately \[calculation 4\] square centimeters.

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