Cannonballs

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 cast?

Correct result:

n₂ =  12

Solution:

$$\begin{gathered} n_1=3 \\ {D}_1=16\text{ cm } \\ {D}_2=10\text{ cm } \\ {r}_1=D_1\mathrm{/}2=16\mathrm{/}2=8\text{ cm } \\ {r}_2=D_2\mathrm{/}2=10\mathrm{/}2=5\text{ cm } \\ {V}_1=n_1\cdot {\displaystyle \frac{4}{3}}\cdot \pi \cdot r_1^3=3\cdot {\displaystyle \frac{4}{3}}\cdot 3.1416\cdot 8^3\doteq 6433.9818{\text{cm}}^3 \\ {V}_2={\displaystyle \frac{4}{3}}\cdot \pi \cdot r_2^3={\displaystyle \frac{4}{3}}\cdot 3.1416\cdot 5^3\doteq 523.5988{\text{cm}}^3 \\ {V}_1=n_2\cdot V_2 \\ {n}_2=\lfloor V_1\mathrm{/}{V}_2\rfloor =\lfloor 6433.9818\mathrm{/}523.5988\rfloor =12 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Balls
  Ping pong balls have a diameter of approximately 5.1 cm. It sold in boxes of 10 pieces: each box has a cuboid shape with a square base. The balls touch the walls of the box. Calculate what portion of the internal volume of the box is filled with balls.
• Clay balls
  How many clay balls with a radius of 1 cm can be made from a ball of clay with a radius of 8 cm?
• Two balls
  Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.
• Thousand balls
  We have to create a thousand balls from a sphere with a diameter of 1 m. What will be their radius?
• Gas sphere
  The gas tank has the shape of a sphere with a diameter of 14 m. How many m³ of gas will fit in it?
• Volume and surface area
  Find the volume and surface of a wooden block with dimensions: a = 8 cm, b = 10 cm, c = 16 cm.
• Cuboids in cube
  How many cuboids with dimensions of 6 cm, 8 cm and 12 cm can fit into a cube with side 96 centimeters?
• Sphere growth
  How many times grow volume of sphere if diameter rises 10×?
• Plasticine ball
  Plasticine balls have radius r₁=85 cm, r₂=60 mm, r₃=59 cm, r₄=86 cm, r₅=20 cm, r₆=76 mm, r₇=81 mm, r₈=25 mm, r₉=19 mm, r₁₀=14 cm. For these balls
• The cuboid
  The cuboid is filled to the brim with water. The external dimensions are 95 cm, 120 cm, and 60 cm. The thickness of all walls and the bottom is 5 cm. How many liters of water fit into the cuboid?
• Balls
  Three metal balls with volumes V₁=71 cm³ V₂=78 cm³ and V₃=64 cm³ melted into one ball. Determine it's surface area.
• Volume of sphere
  How many times does the volume of a sphere increase if its radius increases 2 ×?
• Conva
  How many liters of water fit into the shape of a cylinder with a bottom diameter 20 cm and a height 45 cm?
• Pool coating
  How many pieces of tiles 25 cm × 15 cm need to coat the bottom and side walls of the pool with bottom dimensions 30 m × 5 m, if the pool can fit up to 271500 liters of water?
• The pot
  Diameter of the pot 38 cm. The height is 30 cm. How many liters of water can fit in the pot?
• Concrete box
  The concrete box with walls thick 7 cm has the following external dimensions: length 1.8 m, width 44 cm and height 46 cm. How many liters of soil can fit if I fill it to the brim?
• 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?