To find the volume of the solid shown in the image, we can break it down into a simpler shape. It appears to be a prism with a trapezoidal base. Let's go through the steps to calculate its volume.

1. Calculate the area of the trapezoidal base:

   • The trapezoid has two parallel sides of 4 cm and 6 cm and a height of 3 cm.
   • The area $A$ of a trapezoid is given by: $A = \frac{1}{2} \times ( \text{Base}_1 + \text{Base}_2 ) \times \text{Height}$
   • Substituting the values: $A = \frac{1}{2} \times (4 + 6) \times 3 = \frac{1}{2} \times 10 \times 3 = 15 \, \text{cm}^2$

2. Calculate the volume of the prism:

   • The volume $V$ of a prism is given by: $V = \text{Base Area} \times \text{Height (length of the prism)}$
   • The length of the prism is 5 cm.
   • Substituting the values: $V = 15 \times 5 = 75 \, \text{cm}^3$

Thus, the volume of the solid is $75 \, \text{cm}^3$, which corresponds to option B.

Would you like a deeper breakdown or have any further questions?

Here are 5 related questions to explore further:

1. How is the formula for the volume of a prism derived?
2. What if the solid had a different base shape—how would the calculation change?
3. Can you explain the difference between calculating volume for prisms and pyramids?
4. How would you approach finding the surface area of this solid?
5. What is the significance of the trapezoidal area in other geometric applications?

Tip: Always identify the base area first when calculating the volume of a prism.