Question

these prisms are similar. find the volume of the larger prism in decimal form.

yellow prism:
length = 5 m
volume = 50 m^3

red prism:
length = 7 m
volume = ? m^3

Explanation:

Find the scale factor of the similar prisms

$$ k = \frac{7}{5} = 1.4 $$

Relate the volumes using the scale factor

$$ \frac{V_{\text{larger}}}{V_{\text{smaller}}} = k^3 = (1.4)^3 = 2.744 $$

Calculate the volume of the larger prism

$$ V_{\text{larger}} = 50 \times 2.744 = 137.2\text{ m}^3 $$

Answer:

These prisms are similar. Find the volume of the larger prism in decimal form.

Volume = <blank>137.2</blank> \(\text{m}^3\)