Answered

At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

The volumes of two similar figures are given. The surface area of the larger figure is given. Find the surface area of the smaller figure.
V=648 m^3
V=1536 m^3
S.A.=864 m^2

Sagot :

reinhard10158

Step-by-step explanation:

the volume of a figure bases always on a calculation that multiplies 3 dimensions.

while a surface area bases always on a calculation that multiplies 2 dimensions.

since the figures are similar, that means that all dimensions or side lengths of one figure correlate to the corresponding dimensions or side lengths of the other figure via the same scale factor f.

and that means that

large side length = small side length × f.

and that means that f has to be multiplied in 3 times for the volume and 2 times for the surface area (once for every dimension).

so,

large volume = small volume × f × f × f =

= small volume × f³

1536 = 648 × f³

f³ = 1536/648 = 64/27

f = 4/3

and

large surface = small surface × f×f =

= small surface × f²

small surface = large surface / f² = 864 / 16/9 =

= 864 × 9/16 = 54 × 9 = 486 m²

We appreciate your time. Please come back anytime for the latest information and answers to your questions. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.