Question

The two rectangular prisms are similar. What is the volume of the larger rectangular prism?

Answer 1

The question is missing the figure which is attached below.

Answer:

1620 cm³

Step-by-step explanation:

Given:

The two prisms are similar.

Volume of the smaller prism (V₁) = 60 cm³

Length of the smaller prism (l₁) = 5 cm

Length of the larger prism (l₂) = 15 cm

Now, we know that, for similar figures, the dimensions of the figure are in proportion to each other. Therefore,

$\frac{l_2}{l_1}=\frac{b_2}{b_1}=\frac{h_2}{h_1}=k(constant)\\\\Where,\\b_1,b_2\to\ widths\ of smaller\ and\ larger\ prisms\ respectively\\\\h_1,h_2\to\ heights\ of\ smaller\ and\ larger\ prisms\ respectively$

$\frac{l_2}{l_1}=\frac{15\ cm}{5\ cm}=3\\\\\therefore\ k=3$

This means that, the smaller figure is dilated by a scale factor of 3.

Hence, $l_2=3l_1,b_2=3b_1,h_2=3h_1$

Volume of smaller prism is given as:

$V_1=l_1b_1h_1\\\\l_1b_1h_1=60\ cm^3$

Volume of larger prism is given as;

$V_2=l_2b_2h_2\\\\V_2=3l_1\times 3b_1\times 3h_1\\\\V_2=27(l_1 b_1h_1)\\\\V_2=27\times 60=1620\ cm^3\ \ \ \ [\because\ l_1b_1h_1=60\ cm^3]$

Therefore, the volume of the larger rectangular prism is 1620 cm³.