Question

if the volume of a right rectangular prism is 1.5 cm cubed and its length and width have a product of 1.5cm squared, what is the height of this prism

Answer 1

To find the height of the right rectangular prism, we can use the formula for the volume of a prism:

\[
V = \text{Length} \times \text{Width} \times \text{Height}
\]

We know the volume \( V \) is \( 1.5 \, \text{cm}^3 \), and we are given that the product of the length and width is \( 1.5 \, \text{cm}^2 \). Let's denote:

- Length \( = l \)
- Width \( = w \)
- Height \( = h \)

From the problem, we have:

1. \( l \times w = 1.5 \, \text{cm}^2 \) (Equation 1)
2. \( l \times w \times h = 1.5 \, \text{cm}^3 \)

We can substitute Equation 1 into the volume formula. From the volume formula, we have:

\[
1.5 \, \text{cm}^2 \times h = 1.5 \, \text{cm}^3
\]

To find \( h \), we can divide both sides by \( 1.5 \, \text{cm}^2 \):

\[
h = \frac{1.5 \, \text{cm}^3}{1.5 \, \text{cm}^2} = 1 \, \text{cm}
\]

Thus, the height \( h \) of the prism is:

\[
\boxed{1 \, \text{cm}}
\]