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

no this is a nonlinear negative

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for