Sally needs 480 raspberries to make 4 pies. For each question, explain or show your reasoning. How many raspberries does she need for 10 pies? If Sally uses 720 raspberries. How many pies did she make?

Find the rate of the raspberries needed for 1 pie.

480 / 4 = 120 raspberries

1 pie = 120 raspberries.

How many raspberries does she need for 10 pies?

1 pie = 120 raspberries

10 pies = 120 × 10 (since you need 10 berries, you need to multiply the rate by 10)

10 pies = 1200 raspberries are needed.

If Sally uses 720 raspberries. How many pies did she make?

Since you are figuring out the number of pies, you will divide the number of raspberries by the rate of raspberries in one pie.

720 ÷ 120 = 6 pies.

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.

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step-by-step explanation: