Respuesta :

Alright, lets get started.

Prism A and prism B are similar to each other.

Suppose the dimensions of prism A are : l, w, h

So, the volume of prism A = [tex] l*w*h [/tex]

The dimensions of prism B are half of prism A.

Means , the dimensions of prism B will be : [tex] \frac{l}{2} , \frac{w}{2} , \frac{h}{2} [/tex]

So, volume of prism B = [tex] \frac{l}{2}* \frac{w}{2} *\frac{h}{2} [/tex]

So, volume of prism B = [tex] \frac{1}{8} * (l*w*h) [/tex]

volume of prism B = [tex] \frac{1}{8} * [/tex] volume of prism A

volume of prism B = [tex] \frac{1}{8} * 4320 [/tex]

volume of prism B [tex] = 540 cm^{3} [/tex] : Answer option D

Hope it will help :)

abidemiokin

The volume of prism B is 2160cm³

The ratio is written as a fraction. For instance, a/b is the ratio of a to b.

From the given diagram, we can see that prism A is a scaled copy of prism B.

Get the ratio of the length of the bases;

[tex]Ratio = l_A:l_b\\l_a:l_b = 12:6\\\frac{l_a}{l_b} =\frac{2}{1} \\l_b=\frac{1}{2}l_a[/tex]

This shows that the length of the sides is reduced by a ratio of 2.

Given the volume of prism A = 4320 cm³, using the same ratio to get the volume of prism B as shown

[tex]V_b=\frac{1}{2}V_a \\V_b=\frac{1}{2}\times 4320\\V_b= 2160cm^3[/tex]

Hence the volume of prism B is 2160cm³

Learn more on the volume of prisms here: https://brainly.com/question/23741714

Otras preguntas