Question

use the rules for working with measurements to give your answer to the appropriate accuracy and/or precisio
find the volume of the figure (in $mm^{3}$).

$mm^{3}$

Explanation:

Step1: Recall the volume formula for a pyramid

The volume formula for a pyramid is \( V=\frac{1}{3}Bh \), where \( B \) is the base area and \( h \) is the height. For a rectangular - based pyramid, \( B = l\times w \), with \( l = 117\space mm \) and \( w = 103\space mm \), and \( h=36.0\space mm \).

Step2: Calculate the base area \( B \)

\( B=l\times w=117\times103 = 117\times(100 + 3)=117\times100+117\times3=11700+351 = 12051\space mm^{2} \)

Step3: Calculate the volume \( V \)

\( V=\frac{1}{3}Bh=\frac{1}{3}\times12051\times36.0\)
First, \( \frac{1}{3}\times36.0 = 12 \), then \( V=12051\times12=(12000 + 51)\times12=12000\times12+51\times12=144000+612 = 144612\space mm^{3} \)

Answer:

\( 144612\space mm^{3} \)