Volume and Width
REDESIGNING THE SMARTIES BOX
The Smarties Company is experimenting with new dimensions for its Smarties box. They want to keep the same box design, and have the same amount of chocolate, but they are trying to reduce the amount of cardboard used – it’s expensive.
The aim of this project is to create a new Smarties box size/design that uses a smaller amount of cardboard than the first model, but it needs to have the same volume as the original model.
Q1. Use a piece of A4 paper to make a box with a length of 10cm and a width of 3cm. Then find the volume of the box and the total surface area of the paper used to make the box.
T.S.A: 5 rectangles and 4 squares
5 x L x W + 4W
= 5 x 10 x 3 + 4 x 9
= 186cm
Volume: 5 rectangles and 4 squares
L x W x H
= 10 x 3 x 3
= 90cm
Q2. Make another box with the same general shape, but chose a different length and width. Then find the volume of the box and the total surface area of the paper used.
T.S.A: 5 rectangles and 4 squares
= 5 x 4 x 2 + 4 x 4
= 40 + 16
= 56cm
Volume: L x W x H
= 4 x 2 x 2
= 16cm
Q3. Calculate the volume and the total surface area for each of the boxes in the table below.
Width
Length
Volume
Total surface area
1
10
10cm
54cm
2
10
40cm
116cm
3
10
90cm
186cm
4
10
160cm
264cm
5
10
250cm
350cm
Q4. This graph shows the volume of the different boxes shown in question 3.
Q5. This graph shows the area of the different boxes shown in question 3.
Q6. There’s an idea that the total length and the width should be 10, and that these boxes might have different volumes. Calculate the volume for each of these boxes.
Width
Length
Volume
1
9
9cm
2
8
32cm
3
7
63cm
4
6
96cm
5
5
125cm
6
4
144cm
7
3
147cm
8
2
128 cm
9
1
81cm
Q7. This graph shows the volume of the different boxes displayed in question 6.
Q8. Which of the boxes has the greatest volume? : The box with the greatest volume is the box with a width of 7cm a length of 3 cm and a
The Smarties Company is experimenting with new dimensions for its Smarties box. They want to keep the same box design, and have the same amount of chocolate, but they are trying to reduce the amount of cardboard used – it’s expensive.
The aim of this project is to create a new Smarties box size/design that uses a smaller amount of cardboard than the first model, but it needs to have the same volume as the original model.
Q1. Use a piece of A4 paper to make a box with a length of 10cm and a width of 3cm. Then find the volume of the box and the total surface area of the paper used to make the box.
T.S.A: 5 rectangles and 4 squares
5 x L x W + 4W
= 5 x 10 x 3 + 4 x 9
= 186cm
Volume: 5 rectangles and 4 squares
L x W x H
= 10 x 3 x 3
= 90cm
Q2. Make another box with the same general shape, but chose a different length and width. Then find the volume of the box and the total surface area of the paper used.
T.S.A: 5 rectangles and 4 squares
= 5 x 4 x 2 + 4 x 4
= 40 + 16
= 56cm
Volume: L x W x H
= 4 x 2 x 2
= 16cm
Q3. Calculate the volume and the total surface area for each of the boxes in the table below.
Width
Length
Volume
Total surface area
1
10
10cm
54cm
2
10
40cm
116cm
3
10
90cm
186cm
4
10
160cm
264cm
5
10
250cm
350cm
Q4. This graph shows the volume of the different boxes shown in question 3.
Q5. This graph shows the area of the different boxes shown in question 3.
Q6. There’s an idea that the total length and the width should be 10, and that these boxes might have different volumes. Calculate the volume for each of these boxes.
Width
Length
Volume
1
9
9cm
2
8
32cm
3
7
63cm
4
6
96cm
5
5
125cm
6
4
144cm
7
3
147cm
8
2
128 cm
9
1
81cm
Q7. This graph shows the volume of the different boxes displayed in question 6.
Q8. Which of the boxes has the greatest volume? : The box with the greatest volume is the box with a width of 7cm a length of 3 cm and a