A pyramid has a height of 5 in. and a surface area of 90 in^2. Find the surface area of a similar pyramid with a height of 10 in. Round to the nearest tenth, if necessary.
360 in^2
180 in^2
22.5 in^2
3.6 in^2
See Damon's answer.
http://www.jiskha.com/display.cgi?id=1362360405
To solve this problem, we can use the concept of similarity between the two pyramids.
The relationship between the surface areas of similar figures is given by the square of the ratio of their corresponding lengths. In this case, the length in question is the height of the pyramids.
The ratio of the heights of the two pyramids is 10/5 = 2.
Now, let's find the ratio of their surface areas:
Surface Area Ratio = (height ratio)^2
= 2^2
= 4
Since the surface area of the original pyramid is 90 in^2, we can calculate the surface area of the similar pyramid using the ratio we found:
Surface Area of Similar Pyramid = Surface Area of Original Pyramid × Surface Area Ratio
= 90 × 4
= 360 in^2
Therefore, the surface area of the similar pyramid with a height of 10 inches is 360 in^2