Question

a storage chest has the shape of a rectangular prism with the dimensions shown. the volume of the storage chest is 11,592 cubic inches. what is its height? image of a rectangular prism with length 46 in., width 12 in., and height unknown the height of the storage chest is blank inches.

Explanation:

Step1: Recall volume formula for rectangular prism

The volume \( V \) of a rectangular prism is given by \( V = l \times w \times h \), where \( l \) is length, \( w \) is width, and \( h \) is height. Here, \( l = 46 \) in, \( w = 12 \) in, \( V = 11592 \) cubic inches. We need to find \( h \).

Step2: Rearrange formula to solve for \( h \)

From \( V = l \times w \times h \), we can solve for \( h \) by dividing both sides by \( l \times w \). So, \( h=\frac{V}{l\times w} \).

Step3: Substitute values into the formula

Substitute \( V = 11592 \), \( l = 46 \), and \( w = 12 \) into the formula. First, calculate \( l\times w = 46\times12 = 552 \). Then, \( h=\frac{11592}{552} \).

Step4: Perform the division

Divide \( 11592 \) by \( 552 \): \( 11592\div552 = 21 \).

Answer:

21