Question

Find the volume of the following solid:

Answer 1

390cm³

Explanation:

IF you look at the figure attached, you will see that your figure is made up of 3 rectangular prisms.

All you need to do is solve for the volume of each prism and add them up together.

The formula to use to get the volume of a rectangular prism is:

`V=whl`

Where:

V = Volume

w = width

l = length

h = height

Let's get the first one and double it because you have rectangular prisms with the same dimensions:

`V = wlh\\\\V= (5cm)(2cm)(12cm) = 120cm^3\\\\120cm^3 * 2=240cm^3`

Next we get the rectangular prism in the middle:

Notice that the height of the side rectangular prisms is 12 cm. To get the height of the middle figure, just subtract 5cm and 2 cm from the height because they are the excess of the middle.

12cm - (5cm + 2cm)

12 cm - 7cm = 5cm

Then we plug it into the formula

`V = wlh\\\\V= (5cm)(6cm)(5cm) = 150cm^3`

Now that we have the volumes of all figures, just add them up together:

150cm³ + 240cm³ = 390cm³