Question

question
find the volume of a rectangular prism with a length of 13.2 in, a width of 13.8 in and a height of 15.9 in, to the nearest tenth of a cubic inch.

Explanation:

Step1: Recall the volume formula

The volume \( V \) of a rectangular prism is \( V = l\times w\times h \), where \( l \) is length, \( w \) is width, and \( h \) is height.

Step2: Substitute the given values

Given \( l = 13.2\), \( w = 13.8\), \( h = 15.9\). Then \( V=13.2\times13.8\times15.9\).
First, calculate \(13.2\times13.8 = 182.16\).
Then, \(V = 182.16\times15.9\).
\(182.16\times15.9=(180 + 2.16)\times15.9=180\times15.9+2.16\times15.9\).
\(180\times15.9 = 2862\), \(2.16\times15.9=(2 + 0.16)\times15.9=2\times15.9+0.16\times15.9 = 31.8+2.544 = 34.344\).
\(V=2862+34.344=2896.344\).

Step3: Round to the nearest tenth

The digit in the hundredth place is \(4\). Using the rounding rule (if the digit in the hundredth place \(<5\), we keep the digit in the tenth place as it is). So \(2896.344\approx2896.3\).

Answer:

\(2896.3\) cubic inches.