Find the length of the base of a square pyramid if the volume is 1,024 cubic inches and has a height of 12 inches. Use 3.14 for pi and round your answer to the nearest hundredth.

4 inches

8 inches

16 inches

24 inches

Question

Find the length of the base of a square pyramid if the volume is 1,024 cubic inches and has a height of 12 inches. Use 3.14 for pi and round your answer to the nearest hundredth.

 4 inches

 8 inches

 16 inches

 24 inches

anonymous · Answer

@ganeshie8 
@phi 
@jojo4eva 


Please help

phi · Answer

what is the formula for the volume of a pyramid?

anonymous · Answer

attachment

anonymous · Answer

@phi

phi · Answer

that looks like a cone. You want the formula for a square pyramid.

anonymous · Answer

@phi

phi · Answer

OK, can you post the equation for the volume of a square pyramid?

anonymous · Answer

1/3 times b squared times H

phi · Answer

you show write down the entire equation, because we are going to use it to answer the question.

phi · Answer

and use math not words

anonymous · Answer

(1/3) b h

phi · Answer

an equation has an = sign in it

anonymous · Answer

V=(1/3) b h

anonymous · Answer

@phi

phi · Answer

Now  we are ready.
they tell you
 volume is 1,024
height of 12 inches

replace the letters in your equation with those numbers.  what do you get ?

phi · Answer

and somehow your b^2 lost its 2

anonymous · Answer

1,024=(1/3) B2 12

phi · Answer

you should write B^2  (btw B is the side of the square... what you are trying to find)
I would have used x  or s for the side of the square...

your equation is
$$ 1024 = \frac{1}{3} b^2 \cdot 12 $$
now you have to solve for b.
First, multiply both sides by 3. what do you get ?

anonymous · Answer

12 times 3 : 36

phi · Answer

No, we don't want to do that.  How about this:  what is 12/3 ?

anonymous · Answer

4

phi · Answer

can you re-write your equation, using that simplification that 12/3 is 4:
$$ 1024 = \frac{1}{3} b^2 \cdot 12 $$

anonymous · Answer

1024=B2*4

phi · Answer

ok, but get used to writing B^2 (because B2 really means B times 2)

now divide both sides by 4.

phi · Answer

like this
$$ \frac{1024}{4} = \frac{4b^2}{4} $$
simplify both sides. on the right side 4/4 is 1
on the left side 1024/4 is 256

to find b (the answer) take the square root of both sides.
(remember that the sqr(b^2) is b )

anonymous · Answer

so my answer would be 16

phi · Answer

yes

anonymous · Answer

thank you can you help me with something else please