Question

the volume of this triangular prism is 700.7 cubic inches. what is the value of u? u = inches submit

Explanation:

Step1: Write the formula for the volume of a triangular prism

The volume \( V \) of a triangular prism is \( V=\text{Base Area}\times\text{Height} \). The base is a triangle with area \( A = \frac{1}{2}\times\text{base}\times\text{height} \). Here, the base of the triangle is \( 13 \) inches and the height of the triangle is \( u \), and the height (length) of the prism is \( 11 \) inches. So \( V=\frac{1}{2}\times13\times u\times11 \).

Step2: Substitute the given volume and solve for \( u \)

Given \( V = 700.7 \) cubic inches. Then \( 700.7=\frac{1}{2}\times13\times u\times11 \). First, calculate \( \frac{1}{2}\times13\times11=\frac{143}{2}=71.5 \). So the equation becomes \( 700.7 = 71.5u \). Then \( u=\frac{700.7}{71.5} \).

Step3: Perform the division

\( u=\frac{700.7}{71.5}=9.8 \)

Answer:

\( 9.8 \)