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Dmitrij [34]
2 years ago
7

What is the volume of this right prism? 96 in³ 60 in³ 48 in³ 44 in³

SAT
1 answer:
boyakko [2]2 years ago
4 0

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; a = 4in
  • Side length b; b = 5in
  • Side length c; c = 3in
  • Height; h = 8in

Volume; V = \ ?

<h3>Volume of right triangular Prism</h3>

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;

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

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

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

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 : brainly.com/question/17208216

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