Question

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

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 area of the base and \( h \) is the height. For a rectangular - based pyramid, \( B = l\times w \) (where \( l \) is the length and \( w \) is the width of the base). Here, \( l = 117\space mm \), \( w=103\space mm \), and \( h = 36.0\space mm \).

Step2: Calculate the area of the base

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

Step3: Calculate the volume

\( V=\frac{1}{3}Bh=\frac{1}{3}\times12051\times36.0\). First, \( \frac{1}{3}\times36.0 = 12.0 \). Then \( V=12.0\times12051=144612.0\space mm^{3} \). Considering the rules for measurements: The least number of significant figures among the given values (\( 117\) (3 significant figures), \( 103\) (3 significant figures), \( 36.0\) (3 significant figures)) is 3. So, \( V = 1.45\times10^{5}\space mm^{3}\) (rounded to 3 significant figures)

Answer:

\( 1.45\times 10^{5}\space mm^{3} \)