Answer:
Option A is correct.
The volume of prism= [tex]\frac{1}{2}x^3[/tex] cubic units
Explanation:
Volume of the right triangular prism(V) is given by the formula:
[tex]V = B \cdot h[/tex] ; where B is the area of the base, and h is the height.
Given: The height of the prism(h) = x unit
The base (B) in the given figure of the prism is the right triangle with legs of length x unit and base x unit.
Area of the right angle triangle is given by: (A) = [tex]\frac{1}{2}bl[/tex] where b is the base and l is the height of the triangle respectively.
Therefore,
B = [tex]\frac{1}{2} (x) \cdot(x)[/tex] = [tex]\frac{1}{2}x^2[/tex] square unit
Substitute the value of base and height in the above given formula of volume of prism,
therefore,
Volume of the prism (V) = Bh cubic unit
=[tex]\frac{1}{2}x^2 \cdot (x)[/tex]
= [tex]\frac{1}{2}x^3[/tex] cubic units
Answer: A. [tex]\frac{1}{2} x^3[/tex]
Step-by-step explanation:
Since, the volume of a prism = Base area × Height of the prism,
According to the given figure,
The prism having base of right triangle having height x and base x,
⇒ [tex]\text{ The Base area of the prism} = \frac{1}{2}\times x\times x = \frac{1}{2}x^2[/tex]
Also, the height of the given prism = x
⇒ [tex]\text{The volume of the given prism} = \frac{1}{2}x^2\times x = \frac{1}{2}x^3[/tex]
⇒ Option A is correct.
