The surface area of a solid is directly proportional to the square of its dimensions, while the volume is directly proportional to the cube of its dimensions.
Let the dimensions of the smaller solid be x, y, and z, and the dimensions of the larger solid be 3x, 3y, and 3z.
Given that the surface area of the smaller solid is 384 yd2 and the surface area of the larger solid is 1057 yd2, we have:
2(xy + xz + yz) = 384
2(9xy + 9xz + 9yz) = 1057
Simplifying these equations, we get:
xy + xz + yz = 192
9xy + 9xz + 9yz = 529
Dividing the second equation by 9, we get:
xy + xz + yz = 529/9
xy + xz + yz = 192
Since both equations share the same value, we have found the dimensions of the smaller solid:
x + y + z = 192/2 = 96
Since the volume of the larger solid is 1795 yd3, we have:
(3x)(3y)(3z) = 1795
27xyz = 1795
xyz = 1795/27
Substitute the values of x + y + z and xyz:
96 * (1795/27) = volume of smaller solid
Volume of the smaller solid = 96 * (1795/27) = 637.777... yd3
Therefore, the volume of the smaller solid is approximately 637.78 yd3.
There are two similar solids. The surface areas are 384 yd 2 and 1057 yd 2 . The volume of the larger solid is 1795 yd 3 . What is the volume of the smaller solid?(1
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