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 edge of the container?

Correct answer:

n =  16

Step-by-step explanation:

$$\begin{gathered} S=300{\text{cm}}^2 \\ h=10\text{ cm } \\ k=90\mathrm{\%}={\displaystyle \frac{90}{100}}=0.9 \\ {h}_1=k\cdot h=0.9\cdot 10=9\text{ cm } \\ {V}_0=S\cdot h=300\cdot 10=3000{\text{cm}}^3 \\ V=k\cdot V_0=0.9\cdot 3000=2700{\text{cm}}^3 \\ {V}_1=20{\text{cm}}^3 \\ {V}_1={\displaystyle \frac{4}{3}}\pi r^3 \\ r=\sqrt[3]{3\cdot V_1\mathrm{/}4\mathrm{/}\pi }=\sqrt[3]{3\cdot 20\mathrm{/}4\mathrm{/}3.1416}\doteq 1.6839\text{ cm } \\ D=2\cdot r=2\cdot 1.6839\doteq 3.3678\text{ cm } \\ D<h_1 \\ {n}_1=(V_0-V)\mathrm{/}{V}_1=(3000-2700)\mathrm{/}20=15 \\ n=\lceil n_1\rceil +1=\lceil 15\rceil +1=16 \end{gathered}$$

Try another example

Related math problems and questions:

• 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?
• Aquarium
  The box-shaped aquarium is 40 cm high; the bottom has dimensions of 70 cm and 50 cm. Simon wanted to create an exciting environment for the fish, so he fixed three pillars to the bottom. They all have the shape of a cuboid with a square base. The base edg
• Water block
  A block with a 50 cm² base is filled with water 5 cm under the edge. How many can sugar cubes with 2 cm edge be thrown into a container that overflow water?
• Hemispherical hollow
  The vessel hemispherical hollow is filled with water to a height of 10 cm =. How many liters of water are inside if the hollow's inside diameter is d = 28cm?
• Cube-shaped container
  The cube-shaped container has a height of 52 cm and a square base. The container was filled to the brim with water, then we immersed a metal cube in it, which caused 2.7 l of water to flow out of the container. After removing the cube from the water, the
• Hectoliters
  How many hectoliters of water is in garden barrel with 90 cm diameter and a height of 1.3 m, if it is filled to 80% of its capacity?
• Water tank
  The water tank has a cylindrical shape with a base diameter of 4.2 m and is 80 cm deep. How many minutes will take fill it 10 cm below the edge of the tank if water flowing 2 liters per second?
• Sphere - parts
  Calculate the area of a spherical cap, which is part of an area with base radius ρ = 9 cm and a height v = 3.1 cm.
• Spherical cap
  Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm². Determine the radius r of the sphere from which the spherical cap was cut.
• Four prisms
  Question No. 1: The prism has the dimensions a = 2.5 cm, b = 100 mm, c = 12 cm. What is its volume? a) 3000 cm² b) 300 cm² c) 3000 cm³ d) 300 cm³ Question No.2: The prism base is a rhombus with a side length of 30 cm and a height of 27 cm. The height of t
• Hemisphere cut
  Calculate the spherical layer's volume that remains from the hemisphere after the 3 cm section is cut. The height of the hemisphere is 10 cm.
• Cylinder in cube
  Into a paper box in the shape of a cube with an edge of 10 cm is placed a can in the shape of a cylinder with a height of 10 cm and touching all the walls of the cube. What % of the volume of the cube does the can take up?
• 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.
• The pot
  The pot is in 1/3 filled with water. Bottom of the pot has an area of ​​329 cm². How many centimeters rises water level in the pot after add 1.2 liters of water?
• 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
• Water cylinder
  Zuzana poured 785 ml of water into a measuring cylinder with a base radius of 5 cm. The water in the cylinder reached a height of 2 cm from the upper edge of the cylinder. How tall is the cylinder? (π = 3.14)
• The cylindrical container
  The container has a cylindrical shape the base diameter 0.8 meters has a content area of the base is equal to the content area of the shell. How many full liters of water can be poured maximally into the container?