Rectangular prism container holds about 1320 ml of water. Its length, width, and height are consecutive whole numbers. One of its dimensions is 10cm. What are the dimensions of the prism
V = L ∙ W ∙ H = 1320 mL
where:
V = Volume
L = Length
W = Width
H = Height
1 mL = 1 cm³
so
V = 1320 cm³
L ∙ W ∙ H = 1320 cm³
Consecutive whole numbers, including 10 can be:
8 , 9 , 10
9 , 10 , 11
10 , 11 , 12
8 cm ∙ 9 cm ∙ 10 cm = 720 cm³
9 cm ∙ 10 cm ∙ 11 cm = 990 cm³
10 cm ∙ 11 cm ∙ 12 cm = 1320 cm³
The dimensions are:
10 cm x 11 cm x 12 cm
Students
Thank you
To find the dimensions of the rectangular prism, we need to use the information given.
Let's assume that the three consecutive whole numbers representing the dimensions are x, x+1, and x+2.
From the given information, we know that one of the dimensions is 10 cm. Let's determine which one it is.
Since the three dimensions are consecutive whole numbers, one of them must be 10. Let's consider three cases:
Case 1: x = 10 cm
In this case, the dimensions would be 10 cm, 11 cm, and 12 cm, and the volume of the prism would be 10 * 11 * 12 = 1320 cm³.
Case 2: x+1 = 10 cm
In this case, the dimensions would be 9 cm, 10 cm, and 11 cm, and the volume of the prism would be 9 * 10 * 11 = 990 cm³, which is less than 1320 cm³.
Case 3: x+2 = 10 cm
In this case, the dimensions would be 8 cm, 9 cm, and 10 cm, and the volume of the prism would be 8 * 9 * 10 = 720 cm³, which is less than 1320 cm³.
Therefore, from these cases, we can conclude that x = 10 cm is the correct value.
So, the dimensions of the rectangular prism are:
Length: 10 cm
Width: 11 cm
Height: 12 cm