Given
The two similar cylinders have diameters 6 m and 5 m respectively.
For similar cylinders.
[tex]\frac{r_2}{r_1}=\frac{h_2}{h_1}[/tex]Explanation
a. The height of cylinder on the left is 36m,
To determine the height on the right .
[tex]\begin{gathered} \frac{3}{2.5}=\frac{36}{h_1} \\ h_1=30m \end{gathered}[/tex]Answer
The height on the right is 30 m.
b.The volume of cylinder on left is 216 cubic m.
To determine the volume of cylinder on right.
[tex]\frac{V_2}{V_1}=\frac{r^3_2}{r_{^31}}[/tex]Substitute the values,
[tex]\begin{gathered} \frac{216}{V_1}=\frac{3^3}{2.5^3} \\ V_{_1}=125m^3 \end{gathered}[/tex]Answer
The volume of cylinder right is 125 cubic m.
c. The surface area of cylinder on left is 468 sq.m.
To determine the surface area of cylinder on right.
[tex]\frac{S_2}{S_1}=\frac{r_2^2}{r_1^2}[/tex]Substitute the values.
[tex]\begin{gathered} \frac{468}{S_1}=\frac{3^2}{2.5^2} \\ S_1=325sq.m \end{gathered}[/tex]Answer
Hence the surface area of cylinder on right is 325 sq.m.