Kat has a recipe for a 10cm square based iced cake of height 5 cm. He wants to scale the recipe down for a 6 cm square based cake tin, by scaling it down all the ingredients to give a smaller cake of the same shape.
Choose the three statements which are true:
A. If the cake is the same shape as the original recipe, its height will be 3 cm.
B. If the original recipe uses five medium eggs, he should use three medium eggs.
C. If the original recipe uses five medium eggs, he should use one medium egg.
D. The area to be iced on top of the scaled down cake will be about a third of that of the original cake.
E. The area to be iced on top of the scaled down cake will be about a fifth of that of the original cake.
F. The area to be iced on top of the scaled down cake will be about 60% of that of the original cake.
Can any one help me on how to work out this question??
I think its B, D and A is this in any way correct ???
If two solids are similar then
a) their corresponding sides are directly proportional
b) their corresponding surface areas are directly proportional to the square of their sides
c) their volumes are directly proportional to the cubes of their sides.
so A is definitely true.
for B and C I would consider the amount of eggs to be a part contributing to the volume, so.... 6^3/10^3=.216
.216 of 5 eggs is appr one egg
let me know what your got with the area parts
To scale down the recipe, we need to consider the ratios between the original and scaled measurements. Let's go through each statement to determine if it is true or false:
A. If the cake is the same shape as the original recipe, its height will be 3 cm.
To scale down the height, we need to find the ratio of the original height to the scaled height. The original height is 5 cm, and the scaled height is what we're trying to find. Since we are scaling down from a 10 cm square to a 6 cm square, the ratio of the original height to the scaled height is 10/6.
We can set up a proportion: 5/scaled height = 10/6. To solve for the scaled height, we cross-multiply and get scaled height = (5 * 6)/10 = 3 cm.
Therefore, statement A is true.
B. If the original recipe uses five medium eggs, he should use three medium eggs.
To scale down the number of eggs, we need to find the ratio of the original cake volume to the scaled cake volume. Since we are scaling down from a 10 cm square to a 6 cm square, the ratio of the original volume to the scaled volume is (10/6)^2.
We can set up a proportion: (5 eggs)/scaled eggs = (10/6)^2. Simplifying, we have (5 eggs)/scaled eggs = 100/36. To solve for scaled eggs, we cross-multiply and get scaled eggs = (36 * 5)/100 = 1.8 eggs.
Since we can't have a fraction of an egg, Kat would need to round this down to 1 medium egg.
Therefore, statement B is false.
C. If the original recipe uses five medium eggs, he should use one medium egg.
Following the same explanation as statement B, we determined that Kat should use approximately 1.8 medium eggs, which would be rounded down to 1 egg.
Therefore, statement C is true.
D. The area to be iced on top of the scaled-down cake will be about a third of that of the original cake.
To find the ratio of the area to be iced on the scaled-down cake to the area of the original cake, we need to find the ratio of their corresponding sides. Since we are scaling down from a 10 cm square to a 6 cm square, the ratio of the area to be iced on the scaled-down cake to the area of the original cake is (6/10)^2.
Simplifying this, we have (area to be iced on scaled-down cake)/area of original cake = (6/10)^2. (6/10)^2 is equal to 0.36, which is approximately one-third.
Therefore, statement D is true.
E. The area to be iced on top of the scaled-down cake will be about a fifth of that of the original cake.
Following the same explanation as statement D, we determined that the ratio is approximately one-third, not one-fifth.
Therefore, statement E is false.
F. The area to be iced on top of the scaled-down cake will be about 60% of that of the original cake.
Following the same explanation as statement D, we determined that the ratio is approximately one-third, not 60%.
Therefore, statement F is false.
Based on these explanations, the correct statements are A, C, and D.