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

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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.

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