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 459 insquared S.A. equals 816 insquared V equals 1792 incubed
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 sides.
Let x be the ratio of the sides of the smaller figure to the larger figure. Therefore, x^2 is the ratio of their volumes.
Given:
Surface area of larger figure = 816 in^2
Surface area of smaller figure = 459 in^2
Volume of larger figure = 1792 in^3
We have:
(459/816) = (x^2)
x^2 = 459/816
x = sqrt(459/816)
x = sqrt(459)/sqrt(816)
x = 21/24
x = 7/8
Now, the volume of the smaller figure can be calculated using the formula for volume:
Volume of smaller figure = (Volume of larger figure) * (x^3)
Volume of smaller figure = 1792 * (7/8)^3
Volume of smaller figure = 1792 * (343/512)
Volume of smaller figure = 119984/512
Volume of smaller figure = 234.375 in^3
Therefore, the volume of the smaller figure is 234.375 cubic inches.
that's wrong
Let's try solving it again.
Let the ratio of the sides of the larger figure to the smaller figure be x.
Given:
Surface area of larger figure = 816 in^2
Surface area of smaller figure = 459 in^2
Volume of larger figure = 1792 in^3
Surface area ratio = (459/816) = (x^2)
Volume ratio = (459/816)*x = (x^3)
x^2 = 459/816
x = sqrt(459/816)
x = sqrt(459)/sqrt(816)
x = 21/24
x = 7/8
Volume of smaller figure = (Volume of larger figure) * (x^3)
Volume of smaller figure = 1792 * (7/8)^3
Volume of smaller figure = 1792 * (343/512)
Volume of smaller figure = 237632/512
Volume of smaller figure = 464.5 in^3
Therefore, the volume of the smaller figure is 464.5 cubic inches.