Question

What is the volume of the figure below if a=6 units and b= 4 units a. 108in^3

B. 228in^3
C. 288in^3
D. 360in^3

Answer 1

First let's calculate the volume of the cube. The formula to calculate the volume of a cube is
`V = a^3`, a being the edge length of the cube. So we need to cube the value of a, which is 6. 6 cubed is 216 cubic units.

Now we need to calculate the volume of the triangular prism. The formula to calculate the volume of a cube is
`V = (1)/(2) b * a * h`, a being the side edge length of the prism, b being the height of the triangular side, and h being the base edge length of the triangular side, if that makes any sense (easier to explain visually). h and a are equal to the given a, which is 6 in this case. And b in the formula is equal to b in the given problem. So we substitute the values into the formula:
`V = ((1)/(2) *4) * 6 * 6 = 2 * 36 = 72` cubic units.

Now we take the sum of both of the figures:

`216 + 72 = \bold{288 \ cubic \ units}`