1. 360 in2
Explanation:
The surface area of a pyramid is given by the formula:
Surface area = 1/2 * perimeter of base * slant height + base area
Since the two pyramids are similar, their corresponding sides are in proportion. Let x be the length of one side of the base of the smaller pyramid, and y be the length of one side of the base of the larger pyramid. Then, we have:
y/x = 2 (since the height of the larger pyramid is twice that of the smaller pyramid)
y = 2x
The ratio of the surface areas of the two pyramids is:
(surface area of larger pyramid) / (surface area of smaller pyramid) = (y^2 / x^2)
= (2x)^2 / x^2
= 4
Therefore, the surface area of the larger pyramid is 4 times that of the smaller pyramid.
Substituting the given values, we have:
Surface area of smaller pyramid = 90 in2
Height of smaller pyramid = 5 in
Using the formula for surface area, we can solve for the length of one side of the base:
90 = 1/2 * (4x) * (sqrt(x^2 + 5^2)) + x^2
Simplifying, we get a quadratic equation:
2x^2 + 10sqrt(x^2 + 25) - 90 = 0
Solving this equation (by using the quadratic formula or a graphing calculator), we get:
x ≈ 4.67 in
Therefore, the length of one side of the base of the larger pyramid is:
y = 2x ≈ 9.33 in
Now, we can use the formula for surface area to find the surface area of the larger pyramid:
Surface area = 1/2 * (4y) * (sqrt(y^2 + 10^2)) + y^2
= 360 in2 (rounded to the nearest tenth)
A pyramids has a height of 5 in and surface area of 90 in2 find the surface area of 90 in2 find the surface area of a similar pyramid with a height of 10 in Round to the nearest tenth if necessary
1. 360 in2
2. 180 in2
3. 22.5 in2
4. 3.6 in2
1 answer
1 answer