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 cm³). 22.4 cm 42.5 cm 42.0 cm cm³ need help? read it

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, \(B = l\times w\). Here, \(l = 42.5\space cm\), \(w=22.4\space cm\), and \(h = 42.0\space cm\).

Step2: Calculate the base area \(B\)

\(B=l\times w=42.5\times22.4\)

$$
LATEXBLOCK0
$$

Step3: Calculate the volume \(V\)

\(V=\frac{1}{3}Bh=\frac{1}{3}\times952\times42.0\)

$$
LATEXBLOCK1
$$

Now, consider the rules for significant figures. The numbers \(22.4\) (three significant figures), \(42.5\) (three significant figures), and \(42.0\) (three significant figures). When multiplying and dividing, the result should have the same number of significant figures as the number with the least number of significant figures among the factors. Here, all numbers have three significant figures.

Answer:

\(13300\space cm^{3}\) (rounded to three significant figures)