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
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"#
