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
area changes as the square of the scale, so the new area is
(10/5)^2 times the old area. 90*4 = 360 in²
To find the surface area of a similar pyramid with a height of 10 inches, we need to use the concept of similarity. Two pyramids are similar if their corresponding sides are proportional.
Since the height of the original pyramid is 5 inches, and the height of the similar pyramid is 10 inches, the ratio of their heights is 10/5 = 2.
The ratio of the surface areas of similar figures is equal to the square of the ratio of their corresponding sides. In this case, since we are dealing with heights, we need to use the square of the height ratio.
The surface area ratio is the square of the height ratio, so it is (2)^2 = 4.
Now, we can find the surface area of the similar pyramid. We know that the surface area of the original pyramid is 90 square inches. We can use this information to set up an equation:
Surface Area of the Similar Pyramid / Surface Area of the Original Pyramid = Surface Area Ratio.
Let "x" represent the surface area of the similar pyramid:
x / 90 = 4.
To find "x," we can cross-multiply:
x = 90 * 4.
x = 360 square inches.
Therefore, the surface area of the similar pyramid with a height of 10 inches is 360 square inches.