Question

1. a rectangular prism has a volume of 3 m³, a length of 30 cm, and a width of 40 cm. what is the height of the prism?

a. 25 cm
b. 25 cm
c. 250 cm
d. 25 m

Explanation:

Step1: Convert volume unit

Since \(1m = 100cm\), then \(1m^{3}=(100cm)^{3}=1000000cm^{3}\). So \(3m^{3}=3\times1000000cm^{3} = 3000000cm^{3}\).

Step2: Use volume formula

The volume formula of a rectangular prism is \(V = l\times w\times h\) (where \(V\) is volume, \(l\) is length, \(w\) is width, \(h\) is height). We need to find \(h\), so \(h=\frac{V}{l\times w}\).
Substitute \(V = 3000000cm^{3}\), \(l = 30cm\), \(w = 40cm\) into the formula: \(h=\frac{3000000}{30\times40}\).
First calculate \(30\times40=1200\), then \(h=\frac{3000000}{1200}=2500cm\). Wait, no, there is a mistake. Let's re - check.
Wait, correct formula: \(V=l\times w\times h\), so \(h = \frac{V}{l\times w}\). Given \(V = 3m^{3}=3000000cm^{3}\), \(l = 30cm\), \(w = 40cm\).
\(h=\frac{3000000}{30\times40}=\frac{3000000}{1200} = 250cm\)

Answer:

C. 250 cm