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 531 in squared S.A. equals 1475 in squared V equals 3250 in cubed
To find the ratio of the surface areas of the two figures, we can use the formula:
(S.A. of smaller figure) / (S.A. of larger figure) = (V of smaller figure) / (V of larger figure)
Let x be the volume of the smaller figure. So, the ratio of the surface areas is:
531 / 1475 = x / 3250
Now, we can solve for x:
x = 3250 * (531 / 1475)
x = 1172.2 in cubed
Therefore, the volume of the smaller figure is 1172.2 in cubed.
wrong! the number should come out even
Let the volume of the smaller figure be V.
Since the two figures are similar, the ratio of their surface areas is proportional to the square of the scale factor, and the ratio of their volumes is proportional to the cube of the scale factor.
Given:
Surface area of larger figure = 1475 in^2
Surface area of smaller figure = 531 in^2
Volume of larger figure = 3250 in^3
Let the scale factor between the two figures be x.
(531 / 1475) = (x)^2
x = sqrt((531 / 1475)) = 0.6
(V / 3250) = (0.6)^3
V = 3250 * 0.6^3
V = 560.52 in^3
Therefore, the volume of the smaller figure is approximately 560.52 in^3.