Question

a composite figure is shown what is the volume of the composite figure

Answer 1

To find the volume of this composite figure, we simply need to take the volume of the large rectangular prism and subtract the volume of the chunk that was taken out of it.

So, we will start by just multiplying for volume of the entire whole prism, which would simply be length * width * height.

10 * 7 = 70

70 * 6 = 420

The volume of the entire figure, without the bit missing, is 420 cubic centimeters.

Now, we need to subtract the volume of the missing piece.

So we will take the volume of the smaller missing piece. We are given the length and width (3 and 6), but we don't know the height. We can find the height, though from the information given. We know that the height of the entire figure is 7, and that the distance from the bottom of the figure to the bottom of the chunk missing is 4, so we can just subtract to find the height of the missing figure.

7 - 4 = 3

And the height of the missing piece is 3.

So now, we can multiply:

3 * 6 = 18

18 * 3 = 54

The missing figure has a volume of 54 cubic centimeters.

Now, we can subtract.

420 - 54 = 366

The composite figure has a volume of 366 cubic centimeters.
Hope that helped! =)

Answer 2

To figure out the volume of the composite figure, break it down into easier, more manageable pieces.

For example, I'd break it down into two rectangles. One 7cm x 4cm x 6cm, and the other 6cm x 4cm x 6cm

Then, you simply find the volume of the two pieces, and add them together.

Volume = lenth x width x height

V = 7 x 4 x 6
V = 168 cubic cm.

V = 6 x 4 x 6
V = 144 cubic cm.

168 + 144 = 312 cubic cm.

The volume of the composite figure is 312 cubic centimeters.