Question

what is the volume of the figure below if a = 9 units and b = 7 units? note: figure is not drawn to scale. a. 364.5 cubic units b. 760.5 cubic units c. 1,296 cubic units d. 1,012.5 cubic units

Explanation:

Step1: Calculate volume of cube

The volume formula for a cube is $V_{cube}=a^3$. Given $a = 9$ units, so $V_{cube}=9^3=9\times9\times9 = 729$ cubic - units.

Step2: Calculate volume of triangular - prism

The base of the triangular - prism is a triangle with base $a = 9$ units and height $b = 7$ units, and the length of the prism is $a = 9$ units. The volume formula for a triangular - prism is $V_{prism}=(\frac{1}{2}\times base\times height)\times length$. Substituting the values, we get $V_{prism}=\frac{1}{2}\times9\times7\times9=\frac{9\times7\times9}{2}=\frac{567}{2}=283.5$ cubic - units.

Step3: Calculate total volume

The total volume $V = V_{cube}+V_{prism}$. So $V=729 + 283.5=1012.5$ cubic - units.

Answer:

D. 1,012.5 cubic units