Answer:
Step-by-step explanation:
Cylinder A:
r = 3 cm
Volume = 27π cm³
[tex]\sf \boxed{\text{Volume of cylinder=$\pi r^2h$}}[/tex]
[tex]\sf \pi*3*3*h = 27 \pi\\[/tex]
[tex]h = \dfrac{27 \pi}{\pi * 3 * 3}\\\\ \boxed{\bf h = 3 \ cm}[/tex]
Cylinder B:
[tex]\sf \r_A : r_B = 3 : 9[/tex][tex]\sf r_A : r_B = 3 : 9[/tex]
= 1 : 3
[tex]\sf h_A : h_B = 1 : 3\\[/tex]
[tex]\sf \dfrac{3}{h_B}=\dfrac{1}{3}\\\\ cross \ multiply,\\\\ 3*3 = 1*h_B\\\\ h_B = 9 \ cm[/tex]
Volume of cylinder B = π * 9 * 9 * 9
= 729π cm³
[tex]\sf V_A : V_B = 27 \pi :729 \pi[/tex]
= 1 : 27
Volume of cylinder A to volume of cylinder B = 1 : 27
