a baker fills a piping bag with frosting to decorate a cake. the bag has the shape aof a cone, and the frosting fills the bag to a height of 12 inches and a diameter of 5 inches. Approximately what volume of frosting in cubic inches does the piping bag contain? Round to the nearest tenth
1/3 * π * (5/2)^2 * 12 ... in^3
To find the volume of the frosting in the piping bag, we can use the formula for the volume of a cone:
Volume = (1/3) * π * r² * h
Where:
- π is a mathematical constant approximately equal to 3.14159
- r is the radius of the cone (half of the diameter)
- h is the height of the cone (the amount of frosting filled in the bag)
Given the diameter of the piping bag is 5 inches, we can find the radius by dividing it by 2:
Radius (r) = 5 inches / 2 = 2.5 inches
The height of the frosting-filled in the bag is given as 12 inches.
Now, we can substitute the values into the formula to calculate the volume:
Volume = (1/3) * 3.14159 * (2.5 inches)² * 12 inches
Simplifying this equation:
Volume = (1/3) * 3.14159 * 6.25 square inches * 12 inches
Volume = (1/3) * 3.14159 * 75 square inches
Volume ≈ 78.54 cubic inches (rounded to the nearest tenth)
Therefore, the piping bag contains approximately 78.54 cubic inches of frosting.