since their volumes are in the ratio of 2^3:1, their areas are in the ratio of 2^2:1.
The larger figure has 4 times the area of the smaller one.
The volumes of two similar figures are given. The surface area of the smaller figure is given. Find the surface area of the larger figure.
V = 5 in3
V = 40 in3
S.A. = 4 in2
2 answers
volume is proportional to the cube of a linear dimension
Area is proportional to the square of a linear dimension
The ratio of the volumes is 40/5 or 8
That means the linear dimensions have the ratio of ∛8 or 2
That means the areas have the ratio of 2² or 4
so the area of the larger s 4 x 4 in² = 16 in²
Area is proportional to the square of a linear dimension
The ratio of the volumes is 40/5 or 8
That means the linear dimensions have the ratio of ∛8 or 2
That means the areas have the ratio of 2² or 4
so the area of the larger s 4 x 4 in² = 16 in²
1 answer