2. the dimensions of the base of a rectangular solid are 5 and 8, and its altitude is 12. a hole, extending…

2. the dimensions of the base of a rectangular solid are 5 and 8, and its altitude is 12. a hole, extending from the upper base to lower base, is in the shape of a triangular prism whose base has an length of 3 and a height of 2.6. determine the volume of the figure to the nearest tenths.

2. the dimensions of the base of a rectangular solid are 5 and 8, and its altitude is 12. a hole, extending from the upper base to lower base, is in the shape of a triangular prism whose base has an length of 3 and a height of 2.6. determine the volume of the figure to the nearest tenths.

Answer

Explanation:

Step1: Calculate rectangular solid volume

$V_{rect} = l \times w \times h = 5 \times 8 \times 12$

Step2: Calculate triangular prism volume

First find triangular base area: $A_{tri} = \frac{1}{2} \times 3 \times 2.6$, then $V_{prism} = A_{tri} \times 12 = \frac{1}{2} \times 3 \times 2.6 \times 12$

Step3: Subtract prism from solid volume

$V_{final} = V_{rect} - V_{prism}$

Answer:

458.4 units³