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.
A.360 in. ^2
B.180 in. ^2
C.22.5 in. ^2
D.3.6 in. ^2
I think the answer is A but I don't know how to write it down on paper to how I get that answer please help me. And am I even right? Thanks in advance.
follow the same method I showed you in your other post with a similar concept
Except here you have areas instead of volumes
Hint: areas of similar shapes area proportional to the square of their corresponding sides.
I'm confused can you please show me how to work it out on paper. Thank you.
90/x = 5^2/10^2
90/x = 25/100 = 1/4
x = 360
To find the surface area of a similar pyramid, you can use the concept of similarity. Similar figures have corresponding sides in proportion to each other.
In this case, the pyramid has a height of 5 inches and a surface area of 90 square inches. Therefore, to find the surface area of the similar pyramid with a height of 10 inches, you need to find the proportion between the heights of the two pyramids.
The proportion between the heights can be found using the formula:
(height of similar pyramid 1 / height of similar pyramid 2) = (surface area of similar pyramid 1 / surface area of similar pyramid 2)
Let's substitute the given values into the formula:
(5 / 10) = (90 / surface area of similar pyramid 2)
To find the surface area of the similar pyramid 2, isolate it by cross-multiplication:
5 * surface area of similar pyramid 2 = 10 * 90
surface area of similar pyramid 2 = (10 * 90) / 5
surface area of similar pyramid 2 = 900 / 5
surface area of similar pyramid 2 = 180 square inches
Therefore, the answer is B. The surface area of the similar pyramid with a height of 10 inches is 180 square inches.