Question

(12 POINTS) What is the volume of this shape?

Answer 1

Your answer would be 180 cm³.

We can treat this solid like a prism and therefore find the area of the cross-section and multiply it by the depth.

To do this we can split up the cross-section into 3 rectangles with dimensions 5 x 4, so we get (5 × 4) × 3 = 20 × 3 = 60 cm².

Then we multiply the cross-section by 3, which gives us 60 × 3 = 180 cm³.

I hope this helps!

Answer 2

We can see that the shape is really just 3 rectangular prisms, which we can separate and find the find the volume of. The leftmost shape has a volume of 3*4*5=60 cm^3, the middle shape has a volume of 5*4*3=60 cm^3, and the rightmost shape has a volume of 3*4*5=60 cm^3. All of the 3 separate shapes have the same volume, so you can just do 60*3, which is 180 cm^3.