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What is the least number of full cylindrical containers needed to completely fill the fish tank?
(look at picture)

What Is The Least Number Of Full Cylindrical Containers Needed To Completely Fill The Fish Tank Look At Picture class=

Sagot :

chetankachana

Answer:

31 cylinders

Step-by-step explanation:

Hello!

Step 1

Let's first find how much water is held by the cylinder. To find this, we must find the volume (amount of space it takes up) of the cylinder

[tex]V = \pi r^ * h\\\\V = \pi (6/2)^2*8\\\\V = \pi* 3^2*8\\\\V = \pi* 9*8\\\\V = 72\pi[/tex]

Step 2

Now let's find the volume of the rectangular prism.

[tex]V = 24*24*12\\\\\\V = 6912[/tex]

Step 3

Now, let's divide the Volume of the fish tank by the cylinder:

[tex]6912 / 72\pi\\\\\\\text{Approx } 30.58\\ = \text{Approx 31 cylinders}[/tex]

Because we can't use half full cylinder, we round up to the nearest whole number: 31

   

Answer:

31 cylinder containers are needed to completely fill the fish tank.

Step-by-step explanation:

The stuffs required to solve this question:

  • Volume of cylinder = πr²h
  • Volume of rectangular prism = lbh

Where r is radius, h is height, l is length and b is breadth. So, now just use these formulae and solve the question.

A cylinder container is given whose height is 8 inches and diameter is 6 inches. We are aware about the fact that radius is half of diameter. So, the radius of the cylindrical container is 3 inches.

Volume of cylindrical container = π × (3)² × (8)

Volume = 72π or 226 (approx.)

Similarly, a rectangular prism is provided whose length, breadth and height is 24, 24 and 12 inches respectively.

Volume of rectangular prism = 24 × 24 × 12

Volume = 6912

'n' is the number of cylindrical containers required to fill the fish tank. So,

→ n = Volume of rectangular prism/Volume of cylindrical container

→ n = 6912/226 = 30.58

→ n = 31 (approx.)

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