Find the length of the base of a square pyramid if the volume is 48 cubic inches and has a height of 9 inches.

Question

mathstudent55 · Answer

Do you know the formula for the volume of a pyramid?

anonymous · Answer

no i forgot

mathstudent55 · Answer

Here it is:

$A_{pyramid} = \dfrac{1}{3}Bh$

where B = area of the base

anonymous · Answer

these are the answers i can choose from:
 4 inches
 8 inches
 16 inches
 24 inches

mathstudent55 · Answer

In this case, the base is a square.
If the side of the square has length s, the area of the base is $s^2$.

Ok so far?

anonymous · Answer

yes

anonymous · Answer

@LiveLaughDie

mathstudent55 · Answer

Now enter all the info we have in the formula.
The side is unknow, s, and the area of the base is $s^2$.
The volume is 48 in^3.
The height is 9 in.

anonymous · Answer

im horrible at this

anonymous · Answer

@tkhunny

mathstudent55 · Answer

$A_{pyramid} = \dfrac{1}{3} Bh$

$48.~in^3 = \dfrac{1}{3} \times s^2 \times 9 ~in.$

Since all units are inches and cubic inches, I'll leave out the units to simplify the problem. Our answer will be in inches.

$48 = \dfrac{1}{3} \times s^2 \times 9$

On the right side, 9/3 = 3, so we have:

$48 = 3s^2$

Divide both sides by 3:

$16 = s^2$

$s^2 = 16$

$s = 4$

The length of the side is 4 in.

anonymous · Answer

thanks u rock :D :D :D