A recipe calls for 1 cup of pured carrots. How many carrots are needed for the recipe? Use a familiar three-dimensional solid as a model when determining the volume of a single carrot. Note that 1 cup= 14.4375 in^3
dimensions of all of the carrots are-
1.25 in across the top of the carrot (the fat end) and 5 in. is the height
In the picture, the carrot is fatter at one end and sharp at the other
1 cup * 1carrot/(π/3 * (1.25/2)^2 * 5) in^3) * 14.4375in^3/cup = 7 carrots
Thank you so much!
To determine how many carrots are needed for the recipe, we first need to find the volume of a single carrot using the given dimensions. The dimensions provided are:
Top width (across the fat end): 1.25 inches
Height: 5 inches
The shape described for the carrot resembles a cone, where the fat end is the base of the cone and the tip is the apex.
The formula for the volume of a cone is given by:
Volume = (1/3) * π * r^2 * h
Where:
r = radius of the base
h = height of the cone
In this case, the top width (1.25 inches) is equivalent to the radius.
Let's calculate the volume of a single carrot using these values:
Radius (r) = 1.25 inches
Height (h) = 5 inches
Volume = (1/3) * π * (1.25 inches)^2 * 5 inches
Now, let's convert the volume from cubic inches to cups using the given conversion factor:
1 cup = 14.4375 in^3
So, we have:
Volume (in cups) = Volume (in in^3) / 14.4375
Now you can calculate the volume of a single carrot and then divide the required volume for the recipe by the volume of a single carrot to find out how many carrots are needed.