A French Fry Stand At The Fair Serves Their Fries In Paper Cones. The Cones Have A Radius Of 2 Inches And A Height Of 6 Inches. It Is A Challenge To F
A french fry stand at the fair serves their fries in paper cones. The cones have a radius of 2 inches and a height of 6 inches. It is a challenge to fill the narrow cones with their long fries. They want to use new cones that have the same volume as their existing cones but a larger radius of 4 inches.
What will the height of the new cones be?
Answer:
1.5 inches
Step-by-step explanation:
First, we need to find out the volume of the cone that was in use.
Volume of a cone can be found using the formula 1/3 πr²h.
Find volume:
Volume = 1/3 πr²h
Volume = 1/3 π(2)²(6) = 8π in³
Now that we know the volume, we can find the new height by applying the formula of the volume one more time and changing the radius to 4 in.
Find the new height:
Volume = 1/3 πr²h
8π = 1/3 π(4)²h
8π = 16π/3 h
h = 8π ÷ 16π/3
h = 3/2 in or 1.5 in
Answer: The new height is 1.5 inches.
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