One of the skylights on the roof of Bianca’s building is in the shape of the solid below.

A rectangular pyramid has a base of 14 inches by 14 inches and a height of 9 inches. A rectangular prism has a length of 14 inches, width of 14 inches, and height of 2 inches.

What is the total volume of air inside the skylight?
392 inches cubed
588 inches cubed
870 inches cubed
980 inches cubed

The answer is option 4.

Step-by-step explanation:

First, you have to find the volume of rectangular pyramid using the formula, V = 1/3×base area×h where base area is the rectangle base and h represents height of pyramid :

base area = length×width

= 14 in × 14 in

= 196 in²

V = 1/3×196×9

= 588 in³

Next, you have to find the volume of rectangle prism using, V = l×w×h where l is length, w is width and h is height :

Let l = 14 in,

Let w = 14 in,

Let h = 2 in,

V = 14×14×2

= 392 in³

Lastly, you have to add up both volumes together to find the total volume of air inside skylights :

V = 588 + 392

= 980 in³