Question

Rectangular prism container holds about 1320 ml of water. Its length, width and height are consecutive whole number. It's dimensions is 10cm. What are the dimensions of the prism ?

Answer 1

`10cm* 11 cm* 12 cm`

Explanation:

We are given that

Volume of water=1320 ml=1320 cubic cm

1ml=1 cubic cm

One dimension of rectangular prism=l=10 cm

Length,width and height are consecutive whole number

Breadth of rectangular prism=x+1

Height of rectangular prism=x+2

Volume of rectangular prism=lbh

Using the formula

`1320=10(x+1)(x+2)`

`x^2+x+2x+2=(1320)/(10)=132`

`x^2+3x+2-132=0`

`x^2+3x-130=0`

`x^2+13x-10x-130=0`

`x(x+13)-10(x+13)=0`

`(x-10)(x+13)=0`

`x-10=0\implies x=10`

`x+13=0\implies x=-13`

x=-13

It is not possible because length cannot be negative.

Length of rectangular prism=10 cm

Breadth of rectangular prism==10+1=11 cm

Height of rectangular prism==10+2=12 cm

Dimensions of the prism is given by

`10cm* 11 cm* 12 cm`