## anonymous one year ago Find the length of the base of a square pyramid if the volume is 48 cubic inches and has a height of 9 inches.

1. mathstudent55

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

2. anonymous

no i forgot

3. mathstudent55

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

4. anonymous

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

5. mathstudent55

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?

6. anonymous

yes

7. anonymous

@LiveLaughDie

8. mathstudent55

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.

9. anonymous

im horrible at this

10. anonymous

@tkhunny

11. mathstudent55

$$A_{pyramid} = \dfrac{1}{3} Bh$$ $$48.~in^3 = \dfrac{1}{3} \times s^2 \times 9 ~in.$$ 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.

12. anonymous

thanks u rock :D :D :D

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