Question

The linear scale factor of two similar solids is given. Then the surface area and volume of the smaller figure are also given. Find the surface area and volume of the large figure.
Scale factor: 4:5

Surface area: 160

volume: 704

Surface area: ?

volume: ?

Answer 1

Answer:

Surface area: 250

Volume: 1375

Step-by-step explanation:

Scale factor: 4:5

This means that the dimensions of the larger figure are 5/4 of those in the smaller figure.

Surface area:

The surface area is found multiplying the square of the change(5/4) by the original surface area(160). So

$S = (\frac{5}{4})^2 \times 160 = \frac{25}{16} \times 160 = 25 \times 10 = 250$

Volume:

The volume is found multiplying the cube of the change(5/4) by the original volume(704). So

$S = (\frac{5}{4})^3 \times 704 = \frac{125}{64} \times 704 = 125 \times 11 = 1375$