Rectangular prism container hold s about 1320ml of water. It's length, width and height are consecutive whole numbers. One of its dimensions is 10cm what are the dimensions of the prism?

Answer: The dimensions of the prism are

10, 11 and 12

Step-by-step explanation:

The volume of the rectangular prism is 1320ml

1 ml = 1 cm^3

Therefore volume is:

V = 1320 cm^3

The volume of a rectangular prism is

V = L * W * H

Since It's length, width and height are consecutive whole numbers. And One of its dimensions is 10cm. Then

1320 = 10 * (n + 1) (n+2) ... (1)

n^2 + 3n + 2 = 132

n^2 + 3n - 130 = 0

Factorise

(n - 10) (n + 13) = 0

n = 10 or - 13

Since it is positive, ignore - 13

n = 10

Substitute n in equation 1

1320 = 10 * 11 * 12

The dimensions of the prism are

10, 11 and 12