A certain square pyramid has a volume of #100 cm^3#. A similar but smaller pyramid has a surface area equal to one fifth of the larger. What is the volume of the smaller pyramid?

1 Answer
Feb 13, 2018

#"volume "=4sqrt5~~8.944" cubic cm"#

Explanation:

#"consider 2 similar figures then"#

#"linear ratios "=a:b#

#"area ratios "=a^2:b^2#

#"volume ratios "=a^3:b^3#

#"here "a^2:b^2=1:5#

#rArra:b=sqrt1:sqrt5=1:sqrt5#

#rArra^3:b^3=1^3:(sqrt5)^3=1:5sqrt5#

#rArr"volume of smaller pyramid "=100/(5sqrt5)#

#rArr"volume "=20/sqrt5xxsqrt5/sqrt5=4sqrt5" cubic cm"#