The volume of the larger cylinder is 54 cm3.
Two cylinders are said to be similar if the ratio of their radii is equal to the ratio of their heights is equal.
Analysis:
let length of radii for smaller and bigger cylinders to be r and R respectively.
let length of height of smaller and bigger cylinder be h and H respectively.
Base area of smaller cylinder = π[tex]r^{2}[/tex] = 24
r = [tex]\sqrt{\frac{24}{\pi } }[/tex]
Base area of bigger cylinder = π[tex]R^{2}[/tex] = 54
R = [tex]\sqrt{\frac{54}{\pi } }[/tex]
volume of smaller cylinder = base area x height
16 cm3 = 24 cm2 x h
h = 16/24 = 2/3m
for similar cylinders, [tex]\frac{r}{R}[/tex] = [tex]\frac{h}{H}[/tex]
[tex]\sqrt{\frac{24}{\pi } }[/tex]/ [tex]\sqrt{\frac{54}{\pi } }[/tex] = 2/3/H
H = 1cm
volume of bigger cylinder = base area x height = 54 x 1 = 54 cm3
In conclusion, the volume of bigger cylinder is 54 cm3
Learn more about similar cylinders: brainly.com/question/18440876
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