find the volume in cubic meters

My approach is to break the solid into parts. One part is a $6 \times 8 \times 6$ cuboid minus $1 \times 2 \times 6$ cuboid and the volume is $6 \times 8 \times 6 - 1 \times 2 \times 6=132~\text{m}^3$ . Another part is a right prism with right triangle bases and altitude of $6$ and the volume is $\dfrac{1}{2} \times 3 \times 3 \times 6 = 18~\text{m}^3$ . The last will be the remaining two congruent right prisms with right triangle bases and altitude of $3$ and the volume is $\dfrac{1}{2} \times 3 \times 3 \times 2 \times 2 = 27~\text{m}^3$ . The required volume is $132+18+27 = \boxed{177~\text{m}^3}$