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We can see that we have a cube and a pyramide. So the total volume would be the volume of the cube plus the volume of the pyramide. So first, we find the volume of the cube by using this formula:
Vcube = x^3 ; where x is the length of the sides of the cube.
Here, we can see that the lenght of the sides of the green cube is 15 ft (x = 15ft). Then we enter it into formula:
Vcube = (15ft)^3 = (15ft)(15ft)(15ft) = 3375 ft^3
Then we need to find the volume of the pyramide by using this expression:
Vpyramide = (Abase)(height)/3 ; Where Abase is the area of the base.
So we can see that the area of the base is a square which its length side is 15 ft. Let's remember
the formula of the area of a square is:
Asquare = x^2 = (15ft)^2 = (15ft)(15ft) = 225 ft^2
Now we need to find the height of the pyramide. Let's notice that we have a right triangle with a hypotenuse of 9 ft and its base would be the half of the length of the square (15ft/2 = 7.5 ft) and its height would be the height of the pyramide. Then we can use Pythagoream theorem:
c^2 = a^2 + b^2 ; c is the hypotenuse, a and b are the other sides of the right triangle (its height and base).
So c = 9 and b = 7.5. Then we solve for a like this:
9^2 = a^2 + 7.5^2 -----------> a = sqrt(81 - 56.25) = 4.97 ft
Finally, we have:
Vpyramide = (225ft^2)(4.97ft)/3 = 372.75 ft^3
Vtotal = Vpyramide + Vcube = 372.75 + 3375 = 3747.75 ft^3
Please let me know if you need any clarification. I'm always happy to answer your questions.
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