Question

What is the least number of full cylindrical containers needed to completely fill the fish tank?

(look at picture)

Answer 1

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

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.)

Answer 2

31 cylinders

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

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

Step 2

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

`V = 24*24*12\\\\\\V = 6912`

Step 3

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

`6912 / 72\pi\\\\\\\text{Approx } 30.58\\ = \text{Approx 31 cylinders}`

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