There are three crowns in the royal cabinet: One for the King, One for the Queen, and one for the Princess. The king's circumference was 21.98 in, the Queen's circumference was 43.96 cm and the Princess' circumference as 392.5 mm. What are the Diameters's for all three crowns?
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just divide all circumferences by three.
circumference = 3Xradius
To find the diameters of the crowns, we need to use the formula for the circumference of a circle:
Circumference = π * Diameter
Let's start by converting all the measurements into a consistent unit. In this case, let's use inches.
Given: King's circumference = 21.98 in
Using the formula, we have:
21.98 = π * Diameter
To find the diameter, we need to isolate it. Divide both sides of the equation by π:
Diameter = 21.98 / π
Now let's find the diameter for the Queen's crown.
Given: Queen's circumference = 43.96 cm
To convert cm to inches, we need to multiply by the conversion factor:
1 cm = 0.3937 inches
Therefore, the Queen's circumference in inches is:
43.96 * 0.3937 = 17.32 in
Using the formula for circumference again:
17.32 = π * Diameter
Divide both sides by π to isolate the diameter:
Diameter = 17.32 / π
Finally, let's find the diameter for the Princess' crown.
Given: Princess' circumference = 392.5 mm
To convert mm to inches, we need to multiply by the conversion factor:
1 mm = 0.03937 inches
Therefore, the Princess' circumference in inches is:
392.5 * 0.03937 = 15.43 in
Using the formula for circumference one more time:
15.43 = π * Diameter
Divide both sides by π:
Diameter = 15.43 / π
So, the diameters for the King's, Queen's, and Princess' crowns are:
King: Diameter = 21.98 / π inches
Queen: Diameter = 17.32 / π inches
Princess: Diameter = 15.43 / π inches
Remember to use the appropriate value of π for your calculations.