Answer:
The volume of the toy box is 25688 cubic centimetres
Step-by-step explanation:
The 6 faces of a rectangular prism are rectangles, each two opposite faces are equal in dimensions, its dimensions are L, W, H, so two faces has dimensions L , W, two faces L , H and two faces W , H
The formula of the volume of it is V = L × W × H
∵ The toy box is shaped a rectangular prism
∵ The toy box is 52 cm long
∴ H = 52 cm
∵ The perimeter of one side is 90
- Perimeter of any rectangle is twice the sum of its dimensions
∴ Twice the sum of two dimensions of the side = 90 cm
- Divide it by 2 to find the sum of the two dimensions
∴ The sum of two dimensions = 90 ÷ 2 = 45 cm
The sum of two dimensions is less than the height of the box, that means 45 is the sum of the other two dimensions L and W
∵ L + W = 45
∵ The height of the box is is twice as long as it’s width
∴ H = 2 W
∵ H = 52 cm
∴ 52 = 2 W
- Divide both sides by 2
∴ 26 = W
∴ W = 26 cm
Substitute the value of W in the equation of the sum of the two dimensions to find L
∵ L + 26 = 45
- Subtract 26 from both sides
∴ L = 19 cm
∵ V = L × W × H
∴ V = 19 × 26 × 52
∴ V = 25688 cm³
The volume of the toy box is 25688 cubic centimetres
