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 answer:

n₂ =  12

Step-by-step explanation:

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

Try another example

Related math problems and questions:

• 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?
• Metal balls
  Four metal balls with a diameter of 5 cm are placed in a measuring cylinder with an inner diameter of 10 cm. What is the smallest water volume to be poured into the cylinder so that all balls are below the water level?
• 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.
• 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?
• Thousand balls
  We have to create a thousand balls from a sphere with a diameter of 1 m. What will be their radius?
• Brass ball
  What is the weight of a hollow brass ball, the outer diameter of which is 16 cm and the wall thickness is 2 cm, while the density of brass is ϱ = 8.5 g
• 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 cylindrical container
  The cylindrical container has a base area of 300 cm³ and a height of 10 cm. It is 90% filled with water. We gradually insert metal balls into the water, each with a volume of 20 cm³. After inserting how many balls for the first time does water flow over
• The inflated
  The inflated gymnastic ball should have a diameter of 65 cm. How many times do we have to pump air into a fully blown ball with a bicycle inflator to inflate it if the working volume of the inflator is a cylinder with an inner diameter of 2 cm and a heigh
• 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.
• Conva
  How many liters of water fit into the shape of a cylinder with a bottom diameter 20 cm and a height 45 cm?
• Volume of sphere
  How many times does the volume of a sphere increase if its radius increases 2 ×?
• The pot
  Diameter of the pot 38 cm. The height is 30 cm. How many liters of water can fit in the pot?