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

Answer:

$10cm\times 11 cm\times 12 cm$

Step-by-step 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

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

$x^2+x+2x+2=\frac{1320}{10}=132$

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

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

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

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

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

$x-10=0\implies x=10$

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

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

$10cm\times 11 cm\times 12 cm$