Answer :
Given:
Given that two similar cylinder have surface areas 24π cm² and 54π cm².
The volume of the smaller cylinder is 16π cm³
We need to determine the volume of the larger cylinder.
Volume of the larger cylinder:
The ratio of the two similar cylinders having surface area of 24π cm² and 54π cm², we have;
[tex]\frac{24 \pi}{54 \ pi}=\frac{4}{9}[/tex]
[tex]=\frac{2^2}{3^2}[/tex]
Thus, the ratio of the surface area of the two cylinders is [tex]\frac{2^2}{3^2}[/tex]
The volume of the larger cylinder is given by
[tex]\frac{2^2}{3^2}\times \frac{2}{3}=\frac{16 \pi }{x}[/tex]
where x represents the volume of the larger cylinder.
Simplifying, we get;
[tex]\frac{2^3}{3^3}=\frac{16 \pi }{x}[/tex]
[tex]\frac{8}{27}=\frac{16 \pi }{x}[/tex]
Cross multiplying, we get;
[tex]8x=16 \pi \times 27[/tex]
[tex]8x=432 \pi[/tex]
[tex]x=54 \pi \ cm^3[/tex]
Thus, the volume of the larger cylinder is 54π cm³