A pyramid is 10 inches tall (center of base triangle to topmost point). Keeping mass unchanged, if a scientist is able to reduce density of pyramid material uniformly by 1/8th of original. What is pyramid's new height?

reduce density of pyramid material uniformly on all sides by 1/8th
huh?

do you mean that the new density of the pyramid is reduced to 1/8th of it's original?

does the pyramid still have the same mass?

(probably doesn't matter) How many sides does the base of the pyramid have?

Does it have 4 sides?  3?  5?

yes 1/8th of original. updated question

 Pyramid still has same mass

6 Sides   ....NOT IMPORTANT

base area remains constant?

then new height is 80 inches.

base area increases also uniformly but not important

80 inches.....NO

oh, then new height is 20 inches

rofl...

"No? Really? Are you sure?

...

10?"

New height is twice original - 20 inches.

10 inches / (1/8)^(1/3) = 20 inches

DJ beat me again to the answer - sorry I was watching Cloverfield when these riddles were posted!

Cloverfield in nine words: "What is it?!" "We're gonna die!" BOOM! Roll credits.

+0.5 Duke Jake, (NO explanation) +0.5 Dorian Gray

mass=density * volume

and volume = 1/3 (length*breadth*hieght which = 1/3 H^3. So, hieght^3 being inversely proportional to density. desnity goes down 1/8th. so hieght doubles. 20cm

Another way of stating the solution:

height2/height1= (volume2/volume1)^(1/3)
= [(mass2/density2)/(mass1/density1)]^(1/3)
= [(mass2/mass1)*(density1/density2)]^(1/3)

But mass2 = mass1, therefore:

height2 = height1/(density2/density1)^(1/3) = 10 inches / (1/8)^(1/3) = 20 inches

The above makes it clear that the shape of the solid is irrelevant. If any solid object remains the same shape but its size is scaled by a factor of (volume2/volume1), all of its linear dimensions scale by a factor of (volume2/volume1)^(1/3).

Cloverfield was such a stupid show...

I was like, all that hype for that?!