Two similar solids have a scale factor of 3:5. If the height of solid 1 is 3cm, what is the height of solid 2?
If the surface area of solid 1 is 54pi cm squared, find the surface area of solid 2.
If the volume of solid 2 is 250pi cm to the 3rd power, find the volume to solid 1.
To find the height of solid 2, we can use the concept of scale factors. The scale factor of 3:5 means that every linear measurement in solid 1 is multiplied by 3/5 to get the corresponding measurement in solid 2.
First, we can set up a proportion based on the scale factor:
(height of solid 1)/(height of solid 2) = 3/5
We know that the height of solid 1 is 3 cm, so we can substitute these values into the proportion:
3/height of solid 2 = 3/5
To solve for the height of solid 2, we can cross-multiply:
3 * 5 = 3 * height of solid 2
Simplifying, we have:
15 = 3 * height of solid 2
Now, divide both sides of the equation by 3 to isolate the height of solid 2:
15/3 = height of solid 2
Calculating, we get:
height of solid 2 = 5 cm
Therefore, the height of solid 2 is 5 cm.