The surface areas of two similar solids are 340 yd2 and 1,158 yd2. the volume of the larger solid is 1,712 yd3. what is the volume of the smaller solid?

Let us say that,

1 = smaller solid

2 = larger solid

We must remember that the surface area of an object is proportional to the square of their sides, therefore,

SA = k s^2

where k is the constant of proportionality.

By taking the ratio of the 2 similar solids:

SA2 / SA1 = k s2^2 / k s1^2

SA2 / SA1 = s2^2 / s1^2

sqrt (SA2 / SA1) = s2 / s1

s2 / s1 = sqrt (1158 / 340)

While the volume of an object is proportional to the cube of their sides, therefore:

V = k’ s^3
where k’ is the constant of proportionality.

By taking the ratio of the 2 similar solids:

V2 / V1 = k’ s2^3/ k’ s1^3

V2 / V1 = s2^3/ s1^3

1712 / V1 = [sqrt (1158 / 340)]^3

1712/V1 = 6.28556705

V1 = 272.37 yd^3

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough