Question

QUESTION 6 An open rectangular cardboard box has the following dimensions: length = 25 cm, breadth = 15 cm and height = x cm. The volume of the box is 3 000 cm³. Fifteen (15) identical cans of cold drink fit snugly into the box, as shown in the diagram below. The box and the cans are of equal height. (Ignore the thickness of the cardboard in your calculations.) 6.1 6.2 6.3 6.4 x cm 15 cm 25 cm Calculate the height of the box. Calculate the radius of a can. If a can is filled to the top, calculate the volume of cold drink contained in the can. Calculate the volume of the space in between all the cans in the box.​

Answer 1

The volume of the space in between all the cans in the box is 642.9cm^3

Calculate the height of the box.

The dimensions of the box are given as:

Length = 25 cm

Width = 15 cm

Height = x cm

Volume = 3000 cm^3

The volume is calculated as:

Volume = Length * Width * Height

So, we have:

25 * 15 * x = 3000

This gives

x = 8

Hence, the height of the box is 8 cm

Calculate the radius of a can. If a can is filled to the top

Here, we have:

Width = 15 cm

Divide by 3 to determine the diameter of a can

Diameter= 5 cm

Divide by 2 to determine the radius of a can

Radius = 2.5 cm

Hence, the radius of the can is 2.5 cm

Calculate the volume of cold drink contained in the can.

This is calculated as:

V = πr²h

So, we have:

V = (22/7) * 2.5^2 * 8

Evaluate

V = 157.14

Hence, the volume of the cold drink in the can is 157.14 cubic feet

Calculate the volume of the space in between all the cans in the box.​

There are 15 boxes in the box.

So, the total volume of the cans is:

v = 15 * 157.14

Evaluate

v = 2357.1

So, the volume of the space in between all the cans in the box is

V = Volume of box - Volume of cans

This gives

V = 3000 - 2357.1

V = 642.9

Hence, the volume of the space in between all the cans in the box is 642.9cm^3

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