Question

volume of a rectangular prism
to find the volume of a rectangular prism, multiply the length by the width by the height.
$v = l \times w \times h$
$v = 0.6 \\, \text{cm} \times 1 \\, \text{cm} \times 2.4 \\, \text{cm}$
$v = 1.44 \\, \text{cm}^3$
calculate the volume of each rectangular prism. be sure to include units in your answer.
a.
\includegraphicsscale=0.5{prism_a.png}
$v = $______
b.
\includegraphicsscale=0.5{prism_b.png}
$v = $______
c.
\includegraphicsscale=0.5{prism_c.png}
$v = $______
d.
\includegraphicsscale=0.5{prism_d.png}
$v = $______
e.
\includegraphicsscale=0.5{prism_e.png}
$v = $______
f.
\includegraphicsscale=0.5{prism_f.png}
$v = $______
g.
\includegraphicsscale=0.5{prism_g.png}
$v = $______
h.
\includegraphicsscale=0.5{prism_h.png}
$v = $______
i.
\includegraphicsscale=0.5{prism_i.png}
$v = $______

Explanation:

Part a

Step1: Identify formula

The formula for the volume of a rectangular prism is \( V = l \times w \times h \), where \( l \) is length, \( w \) is width, and \( h \) is height.

Step2: Substitute values

For part a, \( l = 0.8 \, \text{mm} \), \( w = 0.4 \, \text{mm} \), \( h = 0.2 \, \text{mm} \). Substitute into the formula: \( V = 0.8 \times 0.4 \times 0.2 \).

Step3: Calculate

First, \( 0.8 \times 0.4 = 0.32 \), then \( 0.32 \times 0.2 = 0.064 \). So \( V = 0.064 \, \text{mm}^3 \).

Step1: Identify formula

Use \( V = l \times w \times h \).

Step2: Substitute values

Here, \( l = 12.4 \, \text{m} \), \( w = 16 \, \text{m} \), \( h = 16 \, \text{m} \). So \( V = 12.4 \times 16 \times 16 \).

Step3: Calculate

First, \( 16 \times 16 = 256 \), then \( 12.4 \times 256 = 3174.4 \). Thus, \( V = 3174.4 \, \text{m}^3 \).

Step1: Identify formula

For a cube (a special rectangular prism), \( l = w = h \), so \( V = l^3 \) (or \( l \times w \times h \)).

Step2: Substitute values

Here, \( l = w = h = 0.6 \, \text{km} \). So \( V = 0.6 \times 0.6 \times 0.6 \).

Step3: Calculate

\( 0.6 \times 0.6 = 0.36 \), then \( 0.36 \times 0.6 = 0.216 \). So \( V = 0.216 \, \text{km}^3 \).

Answer:

\( 0.064 \, \text{mm}^3 \)

Part b