The scale factor of two similar solids is 7:5.
8) Find the ratio of volumes.
9) Find the ratio of surface areas.
To find the ratio of volumes and surface areas of two similar solids, you'll need to use the concept of scale factors.
The scale factor is the ratio of corresponding lengths of the two similar solids. In this case, the scale factor is given as 7:5.
8) To find the ratio of volumes of the two solids, you need to cube the scale factor. This is because volume is a three-dimensional measurement and involves multiplying the length, width, and height of an object.
The ratio of volumes of the two similar solids will be (7/5)^3 = (343/125). So, the ratio of volumes is 343:125.
9) To find the ratio of surface areas of the two similar solids, you need to square the scale factor. This is because surface area is a two-dimensional measurement and involves calculating the area of the faces of an object.
The ratio of surface areas of the two similar solids will be (7/5)^2 = (49/25). So, the ratio of surface areas is 49:25.
To find the ratio of volumes, we need to cubically scale the ratio of the lengths (or sides) of the solids.
The scale factor is 7:5, so the ratio of volumes is (7^3):(5^3), which simplifies to 343:125.
Therefore, the ratio of volumes is 343:125.
To find the ratio of surface areas, we need to square scale the ratio of the lengths (or sides) of the solids.
The scale factor is 7:5, so the ratio of surface areas is (7^2):(5^2), which simplifies to 49:25.
Therefore, the ratio of surface areas is 49:25.