Question

the volume of the triangular block is 4 cubic inches. what is the approximate length of y? round to the nearest tenth of an inch.
1.4 in.
2.0 in.
2.8 in.
3.5 in.

Explanation:

Step1: Find base area (right triangle)

The base is a right triangle with legs $x$, so area $A = \frac{1}{2}x^2$.

Step2: Set up volume formula

Volume $V = A \times x = \frac{1}{2}x^3$. Substitute $V=4$:
$$4 = \frac{1}{2}x^3$$

Step3: Solve for $x$

Multiply both sides by 2: $x^3 = 8$, so $x = \sqrt[3]{8} = 2$ in.

Step4: Calculate $y$ (hypotenuse)

Use Pythagorean theorem: $y = \sqrt{x^2 + x^2} = \sqrt{2x^2}$. Substitute $x=2$:
$$y = \sqrt{2(2)^2} = \sqrt{8} \approx 2.8$$

Answer:

2.8 in.