Since the figures are similar, we know that the ratio of their surface areas is equal to the square of the ratio of their corresponding side lengths.
Let x be the ratio of the side lengths of the larger figure to the smaller figure. We can set up the proportion:
(216) / (1350) = x^2
Solving for x, we get:
x = sqrt(216/1350)
x = sqrt(0.16)
x = 0.4
So, the side lengths of the larger figure are 0.4 times the side lengths of the smaller figure.
To find the volume of the smaller figure, we can set up another proportion using the volume ratio:
(3125) / (V) = (0.4)^3
Solving for V, we get:
V = 3125 / (0.4)^3
V = 3125 / 0.064
V = 48,828.125 in^3
Therefore, the volume of the smaller figure is 48,828.125 cubic inches.
The surface areas of two similar figures are given. The volume of the larger figure is given. Find the volume of the smaller figure.
S.A.
equals
216 insquared
S.A.
equals
1350 insquared
V
equals
3125 incubed
1 answer