# Circle + volume - math problems

1. Pentagonal prism The regular pentagonal prism is 10 cm high. The radius of the circle of the described base is 8 cm. Calculate the volume and surface area of the prism.
2. What is bigger? Which ball has a larger volume: a football with a circumference of 66 cm or a volleyball with a diameter of 20 cm?
3. Tunnel boring How much material did they dig when cutting the 400m long tunnel? The content of the circular segment, which is the cross section of the tunnel is 62m2.
4. The Earth The Earth's surface is 510,000,000 km2. Calculates the radius, equator length, and volume of the Earth, assuming the Earth has the shape of a sphere.
5. Hexa pyramid The base of the regular pyramid is a hexagon, which can be described by a circle with a radius of 1 m. Find the volume of the pyramid 2.5 m high.
6. Cylinder and its circumference If the height of a cylinder is 4 times its circumference c, what is the volume of the cylinder in terms of its circumference, c?
7. The cylinder 2 Find the volume and the lateral area of a cylinder of height 12 inches and a base radius of 4 inches.
8. Steel tube The steel tube has an inner diameter of 4 cm and an outer diameter of 4.8 cm. The density of the steel is 7800 kg/m3. Calculate its length if it weighs 15 kg.
9. Ratio of volumes If the heights of two cylindrical drums are in the ratio 7:8 and their base radii are in the ratio 4:3. What is the ratio of their volumes?
10. Metal tube Calculate the metal tube mass 8dm long with the outer radius 5cm and the inner radius 4.5cm and 1cm3 of this metal is 9.5g.
11. Cube into cylinder If we dip a wooden cube into a barrel with a 40cm radius, the water will rise 10 cm. What is the size of the cube edge?
12. The diagram 2 The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm2. Calculate correct to 3 significant figures: *Base Radius *Height *Volume of the cone
13. The pot The pot is a cylinder with a volume of V = 7l and an inner diameter of d = 20cm. Find its depth.
14. Iron density Calculate the weight of a 2 m long rail pipe with an internal diameter of 10 cm and a wall thickness of 3 mm. The iron density is p = 7.8 g/cm3.
15. Height as diameter of base The rotary cylinder has a height equal to the base diameter and the surface of 471 cm2. Calculate the volume of a cylinder.
16. Collect rain water The garden water tank has a cylindrical shape with a diameter of 80 cm and a height of 12 dm. How many liters of water will fit into the tank?
17. Slant height The slant height of cone is 5cm and the radius of its base is 3cm, find the volume of the cone
18. 3d printer 3D printing ABS filament with diameter 1.75 mm has density 1.04 g/cm3. Find the length of m = 5 kg spool filament. (how to calculate length)
19. Perimeter of base The circumference of the base of the rotating cylinder is same as its height. What is the diameter and height of this cylinder with volume 1 liter?
20. A pipe A radius of a cylindrical pipe is 2 ft. If the pipe is 17 ft long, what is its volume?

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