A specialty cooking oil is packaged in a bottle that is a triangular prism. The base of the bottle is 2.2 in. Wide and 2.4 in. High; the bottle is 6 in. Tall. The glass is 0.2 in. Thick. What is the interior volume of the bottle?
Thank you
assuming the dimensions are the outside dimensions, then
v = (1/2)(2.2-2*0.2)(2.4-2*0.2)(6-2*0.2) = 10.08
i don't now
I AM A FASHION DESIGNED NOT A MATH TEACHER
To find the interior volume of the triangular prism bottle, we need to calculate the volume of the prism excluding the thickness of the glass.
First, let's calculate the volume of the triangular prism. The formula for the volume of a prism is V = Bh, where B is the base area and h is the height of the prism.
In this case, the base of the prism is a triangle with a base length of 2.2 in and a height of 2.4 in. So, the base area (B) can be calculated as 0.5 * base length * height of triangle.
B = 0.5 * 2.2 in * 2.4 in = 2.64 in²
Now, we need to calculate the height of the prism, which is the same as the height of the bottle. The height (h) is given as 6 in.
Next, we can calculate the volume of the prism (interior volume of the bottle) using the formula:
V = Bh = 2.64 in² * 6 in = 15.84 in³
However, we need to subtract the volume occupied by the glass, which is the volume of a triangular prism with the same dimensions as the bottle but smaller. The thickness of the glass is given as 0.2 in.
Using the same base area (B) and height (h), we calculate the volume of the glass:
V_glass = B * h = 2.64 in² * 0.2 in = 0.528 in³
Finally, we subtract the volume of the glass from the interior volume of the bottle:
Interior Volume = V - V_glass = 15.84 in³ - 0.528 in³ = 15.312 in³
Therefore, the interior volume of the specialty cooking oil bottle is 15.312 cubic inches.