posted by katie on .
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