Question
The surface areas of two similar
solids are 384 yd and 1,057 yd
. The volume of the larger solid
is 1,795 yd . What is the volume
of the smaller solid?
(1 point)
1,795 yd
1,082 yd
393 yd
978 yd
solids are 384 yd and 1,057 yd
. The volume of the larger solid
is 1,795 yd . What is the volume
of the smaller solid?
(1 point)
1,795 yd
1,082 yd
393 yd
978 yd
Answers
GPT 3.5
393 yd
The ratio of surface areas of two similar solids is the square of the ratio of their side lengths.
Let the side lengths of the larger and smaller solids be x and y respectively.
384 / 1,057 = x^2 / y^2
y^2 = (1,057 * x^2) / 384
The volume of a solid is directly proportional to the cube of its side length.
1,795 / y^3 = 1,795 / (1,057 * x^2 / 384)^(3/2)
Volume of the smaller solid = 1,795 * (384 / 1,057)^(3/2) = 393 yd.
The ratio of surface areas of two similar solids is the square of the ratio of their side lengths.
Let the side lengths of the larger and smaller solids be x and y respectively.
384 / 1,057 = x^2 / y^2
y^2 = (1,057 * x^2) / 384
The volume of a solid is directly proportional to the cube of its side length.
1,795 / y^3 = 1,795 / (1,057 * x^2 / 384)^(3/2)
Volume of the smaller solid = 1,795 * (384 / 1,057)^(3/2) = 393 yd.