The volumes of two similar solids are 53 cm3 and 1113 cm3. Which is the ratio of the corresponding sides?

Answer 1

The ratio of the corresponding sides is #0.3625:1#

Similar solids means that all dimensions are proportional and all angles are equal or if it involves circular surfaces, their radii too are proportionals.

In such cases if the ratio of corresponding sides (or dimensions) is say #x#, then their volumes are in the ratio #x^3#. In other words, if ratio of volumes is #v#, then ratio of dimensions (corresponding sides) is #root(3)v#.
It is given that volumes are in the ratio #53/1113=53/(53xx21)=1/21#
Hence ratio of corresponding sides is #root(3)(1/21)=root(3)1/root(3)21=1/2.759=0.3625# or #0.3625:1#
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Answer 2

#1 : root(3)21#

let say the #k# is the ratio of corresponding side, where #l# and #L# are for the length of sides of solid respectively.
#l = kL##-> k = l/L# #l * l * l = kL * kL * kL#
#l^3 = k^3*L^3 # where #l^3 = 53 and L^3 = 1113 #
#53 = k^3 * 1113#
#153/1113 = k^3 #
#1/21 = k^3 #
#root(3)(1/21) = k -> 1/root(3)21#,
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Answer 3

The ratio of the corresponding sides of two similar solids is the cube root of the ratio of their volumes. So, the ratio of the corresponding sides is the cube root of (1113 cm^3 / 53 cm^3), which simplifies to approximately 3.74.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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