Question

A household aquarium tank in the shape of a rectangular prism has a base length of 242424 inches (\text{in})(in)(, start text, i, n, end text, )and a base width of 15\,\text{in}15in15, start text, i, n, end text. The height of the water is 12\,\text{in}12in12, start text, i, n, end text above the base. During cleaning, 900900900 cubic inches of water is removed. What is the absolute value of the change in the height of the water in inches

Answer 1

Answer:

The absolute change in the height of the water is 9.5 inches

Step-by-step explanation:

Given

$l =24in$ --- length

$w = 15in$ --- width

$h =12in$ --- height

$V_1 = 900in^3$ --- the volume removed

Required

The absolute change in the height of the water

First, calculate the base area (b):

$b = l * w$

$b =24in * 15in$

$b =360in^2$

The height of the water that was removed is:

$H = \frac{V_1}{b}$ i.e. the volume of the water removed divided by the base area

$H = \frac{900in^3}{360in^2}$

$H = \frac{900in}{360}$

$H = 2.5in$

The absolute change in height is:

$\triangle H = |h - H|$

$\triangle H = |12in - 2.5in|$

$\triangle H = |9.5in|$

$\triangle H = 9.5in$