Two cones are similar. One has the radius of 3cm the other has a radius of 4cm. What is the scale factor of : 1)the base areas
2)their volumes
1) The scale factor for the base areas of two similar cones is the square of the ratio of their radii.
Given:
Radius of the first cone (r1) = 3 cm
Radius of the second cone (r2) = 4 cm
Scale factor for base areas = (r2^2) / (r1^2)
= (4^2) / (3^2)
= 16 / 9
= 1.7778
Therefore, the scale factor for the base areas is approximately 1.7778.
2) The scale factor for the volumes of two similar cones is the cube of the ratio of their radii.
Given:
Radius of the first cone (r1) = 3 cm
Radius of the second cone (r2) = 4 cm
Scale factor for volumes = (r2^3) / (r1^3)
= (4^3) / (3^3)
= 64 / 27
= 2.3704
Therefore, the scale factor for the volumes is approximately 2.3704.