This recipe makes 18 shortbread fingers. Rose follows this recipe, but only wants to make 3 fingers.
How much of each ingredient does she need?

Recipe: Makes 18
120 g butter
60 g sugar
180 g flour

(I don't know if this is the method you are supposed to use, but I believe you will still get the same answer!)

20 g butter, 10 g sugar, 30 g flour

Step-by-step explanation: First off, if we look at 3 and 18, you notice that three is a factor or 18, going into the number 6 times.

So, if you are making 6 times less of the original amount, divide each measurement by six to give you your answer.

120/6 = 20

60/6 = 10

180/6 = 30

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.