(1) The bottom area and height of a cylinder and a cone are equal respectively, and the volume of the cone is the volume of the cylinder (), and the volume of the cylinder is the volume of the cone ().

(2) The radius of the bottom surface of a straight cylinder is 1 cm and the height is 2.5 cm. Its side area is () square centimeters.

(3) The bottom areas and volumes of the cylinder and the cone are equal respectively. Suppose the height of the cylinder is 6 cm and the height of the cone is () cm.

(4) The cylinder is 4 decimeters high and 40 cubic decimeters in volume, which is 10 cubic decimeter more than the cone with the same bottom. The height of this cone is () decimeter.

(5) The circumference of the bottom surface of the cylinder is 6.28 decimeter, the height is 1.5 decimeter, the surface area is () square decimeter, and the volume is () cubic decimeter.

(6) The circumference of the cone bottom is 12.56 decimeter, the height is 6 decimeter, and the volume is () cubic decimeter.

(7) The diameter and height of the cone bottom are 6 cm, and its volume is () cubic cm.

(8) After a 2-meter-long log was cut into two sections, the surface area increased by 48 square centimeters. The original volume of this log is () cubic centimeters.

(9) Cut a cylinder with a volume of 60 cubic centimeters into the largest cone, and the volume of this cone is () cubic centimeters.

(10) The diameter of the cone bottom is 13 of the diameter of the cylinder bottom. If their heights are equal, then the volume of the cone is cylindrical ().

(1 1) The radius of the cone bottom is 6 cm, the height is 20 cm, and the volume is () cubic cm.

(12) The volume difference between a cylinder with equal base and equal height and a cone is 16 cubic meter. The volume of this cylinder is () cubic meters, and the volume of this cone is () cubic meters.

(13) The sum of the volumes of cylinders and cones with equal bottoms and equal heights is 96 cubic decimeters, the volume of cylinders is () cubic decimeters, and the volume of cones is () cubic decimeters.

(14) Cut the cylinder with the volume of 18 cubic centimeter into the largest cone, and the volume of the cone after cutting is () cubic centimeter.

(15) The radius of the cone bottom is 3cm, the volume is 6.28cm, and the height of this cone is () cm.

(16) A cube container with a side length of 4 decimeters is filled with water and then poured into a cone container with a bottom area of 12 decimeter, and the height of the cone is () decimeter.

2. True or false:

(1) The volume of a cone is 13 of that of a cylinder. ………………………………………( )

(2) There is a cylinder and a cone with the same bottom radius and height. The volume of a cylinder is 6 cubic decimeters, and the volume of a cone is 2 cubic decimeters. ……………………( )

(3) The volume of a cylinder with the same base and height is 23 more than that of a cone. …… ( )

(4) The height of the cone is unchanged, the bottom area is expanded to 6 times, and the volume of the cone is also expanded to 6 times. ……………………………………………………… ( )

(5) The volume of a cone with a bottom radius of 6 cm is equal to the volume of an outline cylinder with a bottom radius of 2 cm. ………………………………………………………… ( )

(6) Roll a rectangular cardboard with a length of 62.8 cm and a width of 3 1.4cm into a cylindrical paper tube (excluding the width of the paste) with a bottom radius of 10cm. …………( )

(7) The base area and height of a cube and a cone are equal, and the volume of this cube is three times that of the cone. ……………………………………………( )

(8) If the side areas of two cylinders are equal, then their bottom perimeters must be equal. ( )

(9) Cut a cuboid block with a length of 8cm, a width of 4cm and a height of 6cm into the largest cylinder, with a volume of100.48cm3............................................... ()

(10) The volume of the cone is 8. 1 cubic decimeter, the height is 0.3 decimeter, and the bottom area is 8 1 square decimeter.

………………………………………………………( )

Third, choose

1, the diameter of the bottom surface of the cylinder and the cone is equal, the height of the cone is three times that of the cylinder, the volume of the cone is 12 cubic decimeter, and the volume of the cylinder is () cubic decimeter.

① 12 ②36 ③4 ④8

2. The volume of the cone is 12 cubic centimeter, the bottom area is 4 square centimeters, and the height is () centimeters.

①3 ②6 ③9 ④ 12

3. The volume of a cone is n cubic centimeters, and the volume of a cylinder with the same height as its bottom surface is () cubic centimeters.

① n ②2n ③3n ④

4. Cut a section of round steel into the largest cone. The cutting part weighs 8kg, and this section of round steel weighs () kg.

①24 ② 16 ③ 12 ④8

5. The volume of a cylinder is larger than that of a cone with the same height as its bottom ().

①13②132 times and 43 times.

6. Divide a cone-shaped wood block with a base diameter of 27 cm and a height of 9 cm into two pieces with the same shape and size, and the surface area is increased by () square cm.

①8 1 ②243 ③ 12 1.5 ④ 125.6

7. Cylinders and cones are equal in height. The sum of their volumes is 36 cubic decimeters, and the volume of the cone is () cubic decimeters.

① 12 ②9 ③27 ④24

8. Cut a cube with a length of 4 decimeters into the largest cylinder, and the volume of this cylinder is () cubic decimeters.

①50.24 ②64 ③ 12.56 ④200.96

Fourth, the application questions

1. The roller of the roller is cylindrical, with a bottom diameter of 1m and a length of 2m. How many roads can you press per roll?

2. A pile of conical yellow sand, with a circumference of 25.12m at the bottom, a height of1.5m, and a weight of1.5t per cubic meter of yellow sand. How many tons does this pile of sand weigh?

3. The freight box is a cuboid with a length of 4m, a width of 1.5m and a height of 4m. It's full of sand. After unloading, the sand accumulates into a cone with a height of1.5m. What is its bottom area?

4. It is known that a cylindrical steel pipe is 30 cm long, with an outer diameter of 15, a wall thickness of 1 cm and a weight of 7.8 grams per cubic centimeter. How much does this steel pipe weigh?

5. A granary full of rice has a conical top and a cylindrical bottom. The circumference of the cylinder bottom is 62.8 meters, the height is 2 meters, and the height of the cone is 1.2 meters ... How many cubic meters of rice can this grain depot hold? If each cubic meter of rice weighs 500 kilograms, how many tons of rice can this grain depot hold? (Keep one decimal place)

6. Cut a cuboid with a square cross section into the largest cone. It is known that the circumference of the cone bottom is 6.28 cm and the height is 5 cm. What is the volume of this cuboid?