Description
Explanation & Answer
Thank you for the opportunity to help you with your question!
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
Review
Review
24/7 Homework Help
Stuck on a homework question? Our verified tutors can answer all questions, from basic math to advanced rocket science!
Similar Content
Related Tags
Robinson Crusoe
by Daniel Defoe
The Restless Wave
by John McCain
Slaughterhouse Five
by Kurt Vonnegut
The Power of Habit - Why We Do What We Do in Life and Business
by Charles Duhigg
Notes from Underground
by Fyodor Dostoyevsky
Shattered - Inside Hillary Clintons Doomed Campaign
by Amie Parnes and Jonathan Allen
The English Patient
by Michael Ondaatje
The Picture of Dorian Gray
by Oscar Wilde
No Exit
by Taylor Adams