The Volumes of two similar figures are given. The surface area of the smaller figure is given. Find the surface area of the larger figure.

V= 27m^3
V= 64m^3
S.A.= 63m^2

@Logan 183.162.1.116

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To find the surface area of the larger figure, we can set up a ratio between the volumes of the two figures and the ratios between the surface areas.

Let's call the surface area of the smaller figure SA1 and the surface area of the larger figure SA2. We are given that:
Volume of the smaller figure = 27m^3
Volume of the larger figure = 64m^3
Surface area of the smaller figure = 63m^2

We can set up the following ratio between the volumes of the two figures:
(27m^3)/(64m^3) = SA1/SA2

Simplifying the above equation, we get:
27/64 = SA1/SA2

To find the surface area of the larger figure (SA2), we need to solve for it. One way to do that is by cross multiplication:
(27)(SA2) = (64)(SA1)

Now, substitute the value of the surface area of the smaller figure (SA1) with 63m^2 (which was given):
(27)(SA2) = (64)(63m^2)

Simplifying the expression, we get:
27(SA2) = 4032m^2

Finally, divide both sides by 27 to isolate SA2:
SA2 = 4032m^2 / 27

Calculating this expression, we find that the surface area of the larger figure (SA2) is approximately 149.33m^2.

Therefore, the surface area of the larger figure is approximately 149.33m^2.

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