Respuesta :
Answer:
4 inches.
Step-by-step explanation:
The formula for the volume of a pyramid is v=1/3bh.
V is the volume of the shape
1/3 is just a rational number or fraction.
b is the area of the base shape of the 3d shape
h is the height of the shape (slant height).
The general formula for the volume of all shapes is V=Bh
V is the volume
B is the area of the base
h is the height of the prism.
In this case, we have a pyramid, so let's use the formula V=1/3Bh.
We know what the volume so 48=?
We can put 1/3 so 48=1/2 times ? times ?.
The base shape of this pyramid is a square, and it has an edge of 6 inches. We need to find the area of that square because it is the area of our base. the formula for finding the area of a square is A=S squared.
A is the area of the shape
S is the side length.
The reason why it is squared is because all sides of a square are equal to each other. Since the base edge is 6 inches, the other edges are 6 inches as well. There are 4 edges in a square.
A= 6 times 6.
A=36.
We have the area of the base, so we can put 48=1/3 times 36 times ?.
We are finding what the slant height is, so let's put the letter "h" to represent the slant height.
Now, 48=1/3 times 36 times h.
All we have to do is solve for h.
First we have to simplify one side of the equation.
To simplify, we have to do 1/3 times 36, or you can do 36 divided by 3. It is your choice. 36 divided by 3 is 12.
Now we have 12h=48.
Isolate h by dividing both sides by 12. 12h divided 12 is h. 48 divided by 12 is 4.
Therefore h=4 inches. The reason we divide both sides is because we have to do the inverse operation of the original equation. For instance 12h=48. To get to 48, you do 12 times h. We take the inverse (opposite) operation of multiplication (division). That will isolate for h.
The slant height of this square pyramid is 4 inches.
Hope this helps. Have a good rest of your day!
