Final answer:
To calculate the number of pieces of candy that can fit into the pyramid-shaped box, we need to find the volume of the pyramid using the formula V=(1/3)*base area*height. By solving for x in the equation (1/3)*x^3 = 165, we can find the length/width/height of the rectangular box and the volume of the pyramid-shaped box. The correct answer is D. 660 pieces of candy.
Step-by-step explanation:
To find out how many pieces of candy can fit into the pyramid-shaped box, we need to calculate the volume of the pyramid. The volume of a pyramid is given by the formula V = (1/3) * base area * height.
Since the base and height of the pyramid are the same as the rectangular box, let's assume the length, width, and height of the rectangular box is x.
Therefore, the volume of the pyramid-shaped box would be V = (1/3) * x^2 * x = (1/3) * x^3
Since we know that the rectangular box can fit 165 pieces of candy, that means the volume of the rectangular box is equal to the volume of 165 pieces of candy. So we have (1/3) * x^3 = 165.
By solving for x, we can find the length/width/height of the rectangular box, and therefore the volume of the pyramid-shaped box. Then we can calculate how many pieces of candy can fit into the new box by dividing the volume of the pyramid by the volume of one piece of candy.
Therefore, the correct answer is D. 660 pieces of candy.