Question

question 15 of 21
what is the volume of the prism given below?
diagram of a prism with dimensions 8, 15, 10
a. 600 units³
b. 520 units³
c. 350 units³
d. 1200 units³

Explanation:

Step1: Identify the prism type (triangular prism)

The base is a triangle with base \( b = 15 \) and height \( h_{triangle}=8 \), and the length of the prism \( l = 10 \).

Step2: Calculate the area of the triangular base

The formula for the area of a triangle is \( A=\frac{1}{2}\times b\times h \). Substituting \( b = 15 \) and \( h = 8 \), we get \( A=\frac{1}{2}\times15\times8 = 60 \) square units.

Step3: Calculate the volume of the triangular prism

The volume of a prism is \( V = A\times l \), where \( A \) is the base area and \( l \) is the length. Substituting \( A = 60 \) and \( l = 10 \), we get \( V=60\times10 = 600 \) cubic units.

Answer:

A. 600 units\(^3\)