Answer :

Answer:

The answer is [tex]48in^{3}[/tex].

Explanation:

Thanks for taking the time to read What is the volume of this right prism A 96 in³ B 60 in³ C 48 in³ D 44 in³. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada

Option C) 48in³ is the correct answer.

Hence, the volume of the right triangular prism is 48in³.

This question is incomplete, the missing diagram is uploaded along this answer.

Given the data in the question;

  • Side length a; [tex]a = 4in[/tex]
  • Side length b; [tex]b = 5in[/tex]
  • Side length c; [tex]c = 3in[/tex]
  • Height; [tex]h = 8in[/tex]

Volume; [tex]V = \ ?[/tex]

Volume of right triangular Prism

Volume is simply the space created when a surface is enclosed , it is the space that a quantity material that can be held.

The volume of a right triangular prism can be expressed as;

[tex]V = \frac{1}{4}h\sqrt{(a+b+c)(b+c-a)(c+a-b)(a+b-c)}[/tex]

To determine the volume of the right triangular prism, we substitute our given values into the expression above.

[tex]V = \frac{1}{4}h\sqrt{(a+b+c)(b+c-a)(c+a-b)(a+b-c)}\\\\V = \frac{1}{4}*8in*\sqrt{(4in+5in+3in)(5in+3in-4in)(3in+4in-5in)(4in+5in-3in)}\\\\V = \frac{1}{4}*8in*\sqrt{(12in)(4in)(2in)(6in)}\\\\V = \frac{1}{4}*8in*\sqrt{576in^4}\\\\V = \frac{1}{4}*8in*24in^2\\\\V = \frac{1}{4} * 192in^3\\\\V = 48in^3[/tex]

Option C) 48in³ is the correct answer.

Hence, the volume of the right triangular prism is 48in³.

Learn more about volume of right triangular prism : https://brainly.com/question/17208216