A pyramid has a height of 5 in. and a surface area of 90 in
Find the surface area of a similar pyramid with a height of 10 in. Round to the nearest tenth, if necessary.
area grows as the square of the linear scale. So, the new area is
90*(10/5)^2 = _____ in^2
To find the surface area of a similar pyramid with a different height, we need to use the concept of similarity. Similar figures have corresponding sides that are proportional to each other.
In this case, we know that the ratio of the heights of the two pyramids is 10 in / 5 in = 2. This means that the height of the second pyramid is twice that of the first pyramid.
Since the height is proportional to the corresponding sides of the pyramid, we can deduce that the corresponding sides of the second pyramid are also twice as long as the corresponding sides of the first pyramid. Let's call the length of the corresponding sides of the first pyramid "x". Then, the length of the corresponding sides of the second pyramid is 2x.
The formula for the surface area of a pyramid is given as:
Surface Area = Base Area + (0.5 * Perimeter of Base * Slant Height)
Since we are only concerned with the change in height, the base area remains the same for both pyramids.
Let's denote the surface area of the first pyramid as A1 and the surface area of the second pyramid as A2.
We can set up the following proportion:
A2 / A1 = (2x)^2 / x^2
A2 / A1 = 4
This tells us that the surface area of the second pyramid is four times that of the first pyramid.
Given that the surface area of the first pyramid is 90 in², we can find the surface area of the second pyramid:
A2 = 4 * A1
A2 = 4 * 90 in²
A2 = 360 in²
Therefore, the surface area of the similar pyramid with a height of 10 in is 360 in².