# Advanced Math If the height of a pyramid is increased by 60% and the length of an arm of a square is reduced by 35%, how much will the size of the pyramid increase or decrease?

If the height of a pyramid is increased by 60% and the length of an arm of a square is reduced by 35%, how much will the size of the pyramid increase or decrease?
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FieniChoonin
The volume of both pyramids.
The volume of the square pyramid is $V=\frac{1}{3}{a}^{2}h$ where a is a one side length of the square of base of the pyramid.
suppose assume that a=10, h=10.
The volume of the pyramid is
$V=\frac{1}{3}{10}^{2}10$
$=\frac{1}{3}\left(1000\right)$
=333.333
suppose height increase 60% and reduce the length of an arm of a square is reduced by 35%.
${h}_{1}=10+\frac{60}{100}\left(1\right)$
=16
${a}_{1}=10-\frac{35}{100}\left(10\right)$
=6.5
Volume of new pyramid is computed as follows,
${V}_{1}=\frac{1}{3}{\left(6.5\right)}^{216}=\frac{1}{3}\left(42.25\right)16$
=225.333
Here, the new volume decreases, the difference of volume is,
$V-{V}_{1}=333.333-225.333$
=108
Thus, the new volume decreases 108 units.
Compute the size of pyramid decreases
$\frac{V-{V}_{1}}{V}×100=\frac{108}{333.333}×100$
$=0.3240003×100$
=32.4
Therefore, the size of new pyramid decreases 32.4%.