Some application questions about triangles trapezoids cylinders and cones are urgent

A cylindrical bucket with a bottom diameter of 50cm and a height of 80cm to find the bucket capacity.

Cylindrical conic application problem.

1. The roller of the roller is a cylinder, and its bottom surface diameter is 1 meter and the length is 2 meters. How much of the road surface can be pressed per rolling week?

2. A pile of conical yellow sand, the circumference of the bottom surface is meters, the height of the meter, each cubic meter of yellow sand weighs tons, how many tons does this pile of sand weigh?

3. A truck box is a cuboid, its length is 4 meters, its width is meters, and its height is 4 meters, filled with a car of sand, and the sand is piled into a conical shape with a height of meters after unloading, and its bottom area is how many square meters?

4. A cylindrical steel pipe, 30 cm long, the outer diameter is 1 5 long, the wall thickness of the pipe is 1 cm, it is known that the steel weight per cubic centimeter is grams, how many grams does this steel pipe weigh?

5. A grain hoard full of paddy, conical on the top and cylindrical on the bottom. The circumference of the bottom surface of the cylinder is measured in meters, the height is 2 meters, and the height of the cone is meters. How many cubic meters of rice can this grain hoard hold?

If each cubic meter of rice weighs 500 kilograms, how many tons of rice can this grain hoard hold? (Keep one decimal place).

6. Cut a square with a cross-section into the largest cone, the circumference of the bottom surface of the cone is known to be centimeters, the height is 5 centimeters, and what is the volume of the cuboid?

7. A cylinder and a cone are equal in height at the bottom, and their volumes differ by cubic centimeters. If the radius of the bottom surface of a cylinder is 2 cm, what is the square centimeter side area of this cylinder?

8. A cylindrical iron bucket without a lid, with a bottom diameter of 30 cm and a height of 50 cm. How many square centimeters of iron sheet is needed to make such a bucket? What is the maximum amount of water you can hold? (The number is kept as an integer).

9. A conical sand pile, with a height of meters, a bottom radius of 5 meters, and a weight of tons per cubic meter of sand. How many tons does this pile of sand weigh? (The number is kept as an integer).

10. The area of a cone and a cylinder is equal. The volume of a cone is known to be the volume of a cylinder. What is the height of the cone in centimeters and what is the height of the cylinder?

1. How many square meters of iron sheet is needed to make a 1-meter-long iron chimney with a bottom diameter of 20 cm?

2. The volume of a cylindrical shape is 30 cubic meters, the bottom area is 15 square meters, and the height is how many meters?

3. A conical sand pile with a bottom area of 15 square meters and a height of 2 meters. How thick can you spread this pile of sand on a road 400 meters long and 3 meters wide?

4. A conical sand pile with a bottom radius of 2 meters and a height of meters. If each cubic meter of sand weighs tons. How many tons does this pile of sand weigh?

5. A cylindrical bucket without a lid, the diameter of its bottom surface is 4 decimeters, and the height is 5 decimeters.

How many square meters of iron sheet do you need to make such a bucket? (The whole square meter is reserved).

If each liter of water weighs 1 kilogram, how many kilograms of water can this bucket hold? (Iron sheet thickness is not counted).

6. A section of cylindrical steel is 5 meters long, cross-cut into two small cylinders, and the surface area of the cylinder increases by 20 square centimeters. If each cubic centimeter of steel weighs grams, how many kilograms does this section of steel weigh? (The number is reserved for whole kilograms).

7. A cylindrical sink with a bottom radius of 8 cm, and a piece of iron is completely submerged in the sink, and when the iron piece is taken out, the water surface drops by 5 cm. What is the volume of this piece of iron in cubic centimeters?

8. A cylindrical shape with a square with a side length of centimeters on the side, how many square centimeters is the surface area of this cylinder?

9. There are 6 cylindrical columns in the lobby of a hotel, 10 meters high, the perimeter of the column is decimeter, all of them should be painted, if the paint fee per square meter is 80 yuan, how much does it cost?

10. A cylindrical wooden segment with a length of 2 meters and a radius of 4 centimeters at the bottom area is divided into 4 cylindrical wooden segments of the same length. How many square centimeters has the surface area increased from the original?

1. A cylindrical oil drum, the radius of the bottom surface measured from the inside is 20 cm, and the height is 3 decimeters. What is the volume of this oil drum?

2. A cylinder, behind the side is a square with a decimeter side. What is the decimeter diameter of the base surface of this cylinder?

3. A cylindrical iron sheet oil drum contains half a barrel of gasoline, and now after pouring out the gasoline 35, there are still 12 liters of gasoline left. If the inner bottom area of this oil drum is 10 square decimeters, what is the height of the oil drum?

(1) A cylindrical cistern with a diameter of 10 meters and a depth of 2 meters. What is the footprint of this cistern? If you apply cement around the perimeter and bottom of the pool, what is the area of cement?

2) How many square meters of iron sheet do you need to make ten cylindrical tin chimneys with a length of 2 meters and a diameter of 8 cm?

3) The roller of the roller is a cylinder, its length is 2 meters, and the radius of the cross-section of the roller is meters. If you rotate every minute for 5 weeks, how much of the road surface can be pressed per minute?

Let the base area and height of the cylinder and the cone be respectively: s and h

Volume of the cylinder = sh

Volume of the cone = (1 3) sh

It can be obtained from the title.

sh-(1/3)sh=

>sh = also due to the surface area of the cylinder = 2s + sh = 2*

The volume of the cone is 1 3 of the cylinder

Their volume can be found based on the volume difference.

The height can be found according to the area of the land.

That's where the surface area comes in.

1. Cast a cylindrical steel with a bottom radius of 4 decimeters and a height of 5 decimeters into a square steel with a cross-section of decimeters, how many decimeters is this and how many decimeters is the square steel?

2. If the height of a cylinder is reduced by 3 cm, the surface area will be reduced by square centimeters, how many square centimeters is the bottom area of this cylinder?

3. A cone and a cylinder are equal in height at the bottom, and the difference in volume is 32 cubic meters. Cylindrical volume? Cone volume?

4. Cut the cylinder with a circumference of centimeters and a height of 10 centimeters into several equal parts, what is the base area of this cuboid?

5. A conical sand pile with a bottom area of square meters and a height of meters. How many meters can be paved with this pile of sand on a 10-meter-wide road with a thickness of 2 centimeters?

6. Divide the bottom surface of a cylinder into several sectors. Then cut along the height to form an approximate cuboid, the surface area is increased by 400 square centimeters compared to the original, the height of the cylinder is 20, this cylinder surface area? Volume? Let's do it first.

I'm sorry, but you didn't finish your first question. I'll answer the second question for you first.

The height of the cone is the distance from the vertex to the center of the base circle.

To find the height of the cone, you can use the volume formula of the cone to one-third of the base area high, but this question is not applicable. In this problem, we need to use a triangle to find the height of the cone. If you cut the cone along the height of the cone, you get an isosceles triangle.

The circumference of the bottom edge of the enclosed cone is two-thirds of the circumference of the piece of paper. The diameter of the base circle can be found by using the perimeter of the bottom edge of the cone. The radius of the round piece of paper is the waist length of the conical section triangle. At this point, you should know how to do it.

Circumference of the round piece of paper: 2 r=18

Circumference of the bottom surface of the cone: 2 3 2 r=12

Diameter of the bottom surface of the cone: 12 2 = 6

The isosceles triangle obtained by the cross-section has a waist length of 9 cm and a bottom edge length of 6 cm.

According to the Pythagorean theorem, the square of 9 - the square of 3 = 72, so the high is 72 under the root number, which is 6 times the root number 2

For the first question, I can help you prove that DF is a circle o tangent, and as for the rest, you have to wait for you to complete the question.

Proof: If od is connected, then od=ob (the radius of the circles is equal) ab=ac

abc=∠acb

od=ob

abc=∠odb

acb=∠odb

od ac and df ac

AFD = ODF = 90° (complementary to the side inner angle) DF is the tangent of the circle O.

I'm sorry, I won't have a few junior ones???

1. The volume of the cone: 1 3 cubic meters).

2. The volume of the cylinder: cubic meters).

3. The height of the cylinder:

I don't even write the title clearly.

A conical wheat pile, the bottom radius is 2 meters, high rice, if these wheat into the same cylindrical grain hoard, only 4 9 of the grain hoard volume, known grain hoard bottom area is 9 square meters, how many meters of grain hoard height?

Cubic meter 4 9 = cubic meter meter.

The cross-section of the round table cannot be obtained as a rectangle;

The section of the cone cannot be given a rectangle;

The cross-section of the cylinder cannot be given an isosceles trapezoid;

When the cross-section of the conglum infiltration pants passes through the 3 faces of the cube, a triangle is obtained, when the cross-section is parallel to a face of the cube, a rectangle is obtained, when the cross-section passes through the apex of the opposite diagonal of a square infiltration simple shape of the cube, after shouting 4 faces, and when it is obliquely intersected with the opposite side, the isosceles trapezoidal shape can be obtained, so D is selected