A cupcake tray has 24 semi-spherical cups that are 6cm in diameter. What volume of mixture is required to fill the tray if each cup is filled level with the top of thr tray?
24 * 1/2 * pi/6 * 6^3 cm^3
To find the volume of mixture required to fill the cupcake tray, we need to find the volume of each cup first.
The cups are semi-spherical, which means they are half of a sphere. The formula for the volume of a sphere is V = (4/3) * π * r^3, where V is the volume and r is the radius.
In this case, the diameter of each cup is given as 6 cm, so the radius (r) is half of the diameter, which is 6/2 = 3 cm.
Plugging the value of the radius into the volume formula:
V = (4/3) * π * (3^3)
= (4/3) * 3.14 * 27
= 113.04 cm^3 (rounded to two decimal places)
Therefore, the volume of each cup is approximately 113.04 cm^3.
Since there are 24 cups in the tray, we can find the total volume of all the cups by multiplying the volume of one cup by the number of cups:
Total volume = 113.04 cm^3 * 24
= 2712.96 cm^3 (rounded to two decimal places)
So, approximately 2712.96 cm^3 of mixture is required to fill the cupcake tray level with the top.