Question

a cylinder has a radius of 3 cm and length of 10cm every dimension of the cylinder. is multiplied by 3 to form a new cylinder. how is the ratio of the volumes related to the ratio of the corresponding dimension

Answer 1

`V_1=\pi radius_1^2length_1\\\\ radius_1=3cm\\length_1=10cm\\\\ V_1=\pi3^2*10=90\pi cm^3\\\\ V_2=\pi\ (3radius_1)^2*3length_1\\ V_2=\pi 9^2*30=2430\pi\ cm^3\\\\ Ratio=(V_1)/(V_2)=(90)/(2430)=(1)/(27)\\\\Ratio:\ 1:27.`