Body volume - 7th grade (12y) - math problems

  1. The water tank
    hydroglobus The water tank has the shape of a sphere with a radius of 2 m. How many liters of water will fit in the tank? How many kilograms of paint do we need to paint the tank, if we paint with 1 kg of paint 10 m2?
  2. AL wire
    vaha2 What is the weight of an aluminum wire 250 m long with a diameter of 2 mm, if the density of aluminum is p = 2700 kg/m cubic. Determine to the nearest gram.
  3. Volume and surface area
    cuboid_2 Find the volume and surface of a wooden block with dimensions: a = 8 cm, b = 10 cm, c = 16 cm.
  4. What is bigger?
    ball_f Which ball has a larger volume: a football with a circumference of 66 cm or a volleyball with a diameter of 20 cm?
  5. Water tank
    nadrz 300hl of water was filled into the tank 12 m long and 6 m wide. How high does it reach?
  6. Oak trunk
    stromy Calculate in tonnes the approximate weight of a cylindrical oak trunk with a diameter of 66 cm and a length of 4 m, knowing that the density of the wood was 800 kg/m³.
  7. Tunnel boring
    tunnel 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.
  8. Cone from cube
    cones The largest possible cone was turned from a 20 cm high wooden cube. Calculate its weight if you know that the density of wood was 850 kg/m3
  9. Rain
    rain Garden shape of a rectangle measuring 15 m and 20 m rained water up to 3 mm. How many liters of water rained on the garden?
  10. Cannonballs
    sphere_Nickel Of the three cannonballs with a diameter of 16 cm, which landed in the castle courtyard during the battle, the castle blacksmith cast balls with a diameter of 10 cm, which fit into the cannons placed on the walls. How many cannonballs did the blacksmith c
  11. The Earth
    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.
  12. Two rectangular boxes
    cuboid_2 Two rectangular boxes with dimensions of 5 cm, 8 cm, 10 cm, and 5 cm, 12 cm, 1 dm are to be replaced by a single cube box of the same cubic volume. Calculate its surface.
  13. The largest
    cylinder_in_cube The largest possible cylinder was cut from a 20 cm cube. What is the volume of this cylinder?
  14. Surface of the cube
    cubes3 Find the surface of the cube that has volume 1/1m3 2/0.001 m3 3/8000 mm3
  15. Half-filled
    hrnec A cylindrical pot with a diameter of 24 cm is half-filled with water. How many centimeters will the level rise if we add a liter of water to it?
  16. Wax candles
    sviecka A company makes wax candles in the shape of a cylinder. Each candle has a diameter of 4 inches and a height of 7 inches. If the company used 7561.12 in3 of wax, how many candles did it make? Use 3.14, and do not round your answer
  17. Height of the cylinder
    valec The cylinder volume is 150 dm cubic, the base diameter is 100 cm. What is the height of the cylinder?
  18. Nádoba
    cube_sphere_in Nádoba tvaru kostky je naplněna vodou do poloviny své výšky. Pokud dolijeme 20 l vody, bude nádoba naplněna do tří čtvrtin své výšky. Jaký je objem celé nádoby?
  19. Volume of the cone
    kuzel Find the volume of the cone with the base radius r and the height v. a) r = 6 cm, v = 8 cm b) r = 0,9 m, v = 2,3 m c) r = 1,4 dm, v = 30 dm
  20. The prison ball
    prisonBall Calculate the density of the material that the prison ball is made from if you know its diameter is 15cm and its weight is approximately 2.3kg. With the help of mathematical-physicochemical tables estimate what material the ball is made from.

Do you have an interesting mathematical word problem that you can't solve it? Submit math problem, and we can try to solve it.



We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...