Final answer:
The volume of the rectangular prism toy box is 52650 cm³.
Step-by-step explanation:
To find the volume of the rectangular prism toy box, we first need to determine the dimensions of the box. We are given that the length of the box is 52 centimeters. The perimeter of one side of the box is 90 centimeters, which means that the sum of all four sides is 90 centimeters. Since there are two pairs of equal sides in a rectangular prism, we can divide 90 by 2 to find the length of each pair of equal sides. Therefore, the length of each pair of equal sides is 45 centimeters. The height of the box is twice as long as its width, so we can divide the length of each pair of equal sides by 2 to find the width of the box. Thus, the width of the box is 22.5 centimeters. Finally, we can calculate the volume of the box by multiplying its length, width, and height: 52 cm x 45 cm x 22.5 cm = 52650 cm³.