Question

problem 11?
the pair of solids is similar. find the volume of each solid. round to the nearest tenth, if necessary.
volume of small solid =
cm³
volume of large solid =
cm³
need help?

Explanation:

Step1: Calculate volume of small solid (rectangular prism)

The formula for the volume of a rectangular prism is \( V = l \times w \times h \). For the small solid, \( l = 4 \, \text{cm} \), \( w = 3 \, \text{cm} \), \( h = 2 \, \text{cm} \).
\( V_{\text{small}} = 4 \times 3 \times 2 \)
\( V_{\text{small}} = 24 \, \text{cm}^3 \)

Step2: Determine scale factor for large solid

Looking at the corresponding side (e.g., height: small is \( 2 \, \text{cm} \), large is \( 6 \, \text{cm} \)), the scale factor \( k = \frac{6}{2} = 3 \). For similar solids, the ratio of volumes is \( k^3 \).

Step3: Calculate volume of large solid

The volume of the large solid is \( V_{\text{large}} = V_{\text{small}} \times k^3 \). Substituting \( V_{\text{small}} = 24 \) and \( k = 3 \):
\( V_{\text{large}} = 24 \times 3^3 \)
\( V_{\text{large}} = 24 \times 27 \)
\( V_{\text{large}} = 648 \, \text{cm}^3 \)

Answer:

Volume of small solid = \( 24 \, \text{cm}^3 \)
Volume of large solid = \( 648 \, \text{cm}^3 \)