Question

1. a rectangular solid measures 5.05 cm by 2.45 cm by 1.50 cm. refer to example exercise 4 and show the calculation for volume of the rectangular solid.

Explanation:

Step1: Recall the volume formula for a rectangular solid

The volume \( V \) of a rectangular solid (also known as a rectangular prism) is given by the formula \( V = l \times w \times h \), where \( l \) is the length, \( w \) is the width, and \( h \) is the height.

Step2: Identify the given dimensions

We are given the length \( l = 5.05 \, \text{cm} \), the width \( w = 2.45 \, \text{cm} \), and the height \( h = 1.50 \, \text{cm} \).

Step3: Substitute the values into the formula

Substitute \( l = 5.05 \), \( w = 2.45 \), and \( h = 1.50 \) into the formula \( V = l \times w \times h \):
\[
V = 5.05 \, \text{cm} \times 2.45 \, \text{cm} \times 1.50 \, \text{cm}
\]
First, multiply \( 5.05 \) and \( 2.45 \):
\[
5.05 \times 2.45 = 12.3725
\]
Then, multiply the result by \( 1.50 \):
\[
12.3725 \times 1.50 = 18.55875
\]
So, the volume \( V = 18.55875 \, \text{cm}^3 \). Depending on significant figures (the least number of significant figures in the given values is three, from \( 1.50 \)), we can round to three significant figures: \( 18.6 \, \text{cm}^3 \). But if we just calculate the product directly, it's \( 18.55875 \, \text{cm}^3 \).

Answer:

The volume of the rectangular solid is \( \boldsymbol{18.56 \, \text{cm}^3} \) (or \( 18.6 \, \text{cm}^3 \) with three significant figures, or \( 18.55875 \, \text{cm}^3 \) as the exact product).