She has already made the cake and it has a diameter of 20 cm and a height of 7cm. We need to tell her how many grams of Maltesers she needs to buy.
Some of our thinking:
- We will need to know the weight of one Malteser. The packet is 40 grams - we will need to count the number of Maltesers and divide to calculate the weight of each Malteser. Or ... we could use miniature scales.
- We need to know the surface area of the cake.
- The two shapes that make up the cake are the circle, which is the top, and a rectangle.
- How are we going to work out the size of the circle? We know the formula for the area of a circle is pi multiplied the radius squared. The radius of the cake is 10cm and pi is round about 3.14 so the area of the circle is 10 x 10 x 3.14 which is 314 cm squared.
- The sides of the cake, if you unfolded it would be a rectangle. The short side of the rectangle is 7cm. The long side of the rectangle is going to be the same as circumference of the circle.
- The formula is diameter multiplied by pi. 20 cm x 3.14 = 62.8 cm. This is the long side of the rectangle. The short side is 7 cm so the area of the rectangle is 439.6 cm squared.
- So the total surface area that needs to be covered by Maltesers is 753.6 cm squared.
- We now need to know the surface area that one Malteser will cover. We thought they would cover a square shape rather than a circle shape.
- We decided to estimate the diameter of a Malteser first. Nadia said 4 cm, Lilli said 1.3 cm, Abby said 2.2 cm, Juliette says 1.5 cm Charlotte says 1.5 cm Alice says 1 cm, Emily says 2.7 cm, Lottie says 3.1 cm, Kate says 1.5 cm, Sarah-Rose says 1.5 cm. Some of us are very optimistic.
- We measured Maltesers before we ate them. The measurements were:
- We added them all together and divided to calculate the average (mean) diameter of a Malteser. It is 1.42 cm so we figured out each Malteser would cover a square approximately 2.016 cm square. We rounded this to 2 cm square.
- There were 20 Maltesers in a 40 grams pack so the average weight of a Malteser is 2 grams.
- To work out the number of Maltesers needed we went 753.6 / 2. This equaled 376.8 Maltesers.
- We need 377 Maltesers and each is 2 grams so we had to multiply 377 by 2 so Ms Pears needs to by 754 grams.