Hayley Chong's answer to -'s Secondary 3 E Maths Singapore question.
Careful here...
Do note that the volume is proportional to BOTH the radius and and height, and for geometrically similar solids, the radius changes in the same ratio as the height does.
We cannot simply conclude that the height ratio is 125 : 729. If this would be true, then the radius of the cylinders must be the same for the volume ratio to also be 125 : 729. This means that the cylinders would only be different in their heights, and as such, they are not geometrically similar (two similar objects have their relevant dimensions drawn to the same scale). One example of geometrically similar objects would be two cylinders A and B where the radius of cylinder A is 7 times that of cylinder B AND the height of cylinder A is 7 times that of cylinder B.
For part (a), a more appropriate value for the height ratio is
(cube root of 125) : (cube root of 729)
which is 5 : 9.
Do note that the volume is proportional to BOTH the radius and and height, and for geometrically similar solids, the radius changes in the same ratio as the height does.
We cannot simply conclude that the height ratio is 125 : 729. If this would be true, then the radius of the cylinders must be the same for the volume ratio to also be 125 : 729. This means that the cylinders would only be different in their heights, and as such, they are not geometrically similar (two similar objects have their relevant dimensions drawn to the same scale). One example of geometrically similar objects would be two cylinders A and B where the radius of cylinder A is 7 times that of cylinder B AND the height of cylinder A is 7 times that of cylinder B.
For part (a), a more appropriate value for the height ratio is
(cube root of 125) : (cube root of 729)
which is 5 : 9.
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