To find the height of solid II, we can set up a proportion using the scale factor:
scale factor of I : scale factor of II = height of I : height of II
Since we know that the scale factor is 3:5, we can set up the proportion as follows:
3:5 = 3 cm : h
To solve for h, we can cross-multiply and then divide:
3 * h = 3 cm * 5
h = (3 cm * 5) / 3
h = 15 cm
Therefore, the height of solid II is 15 cm.
To find the surface area of solid II, we need to use the scale factor to determine the relationship between the surface areas of the two solids.
The relationship between the surface areas of two similar solids is given by the square of the scale factor.
So, if the scale factor between the two solids is 3:5, then the ratio of their surface areas is (3/5)^2.
Let's calculate the surface area of solid II using this ratio:
surface area of II = (3/5)^2 * surface area of I
Given that the surface area of I is 54Ï€ cm^2, we can substitute it into the equation:
surface area of II = (3/5)^2 * 54Ï€ cm^2
Calculating this expression:
surface area of II = (9/25) * 54Ï€ cm^2
surface area of II = 194.4Ï€ cm^2
Therefore, the surface area of solid II is 194.4Ï€ cm^2.
To find the volume of solid I, we need to use the scale factor to determine the relationship between the volumes of the two solids.
The relationship between the volumes of two similar solids is given by the cube of the scale factor.
So, if the scale factor between the two solids is 3:5, then the ratio of their volumes is (3/5)^3.
Let's calculate the volume of solid I using this ratio:
volume of I = (3/5)^3 * volume of II
Given that the volume of II is 250Ï€ cm^3, we can substitute it into the equation:
volume of I = (3/5)^3 * 250Ï€ cm^3
Calculating this expression:
volume of I = (27/125) * 250Ï€ cm^3
volume of I = 54Ï€ cm^3
Therefore, the volume of solid I is 54Ï€ cm^3.