A pyramid has a height of 5 in. and a 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
the answer is A, 360 in2
if linear dimension scales by a factor of k,
area scales by k^2.
To find the surface area of a similar pyramid with a height of 10 in, we can use the concept of similarity.
Two similar pyramids have the same shape, but their sizes are proportional. Since the height of the first pyramid is 5 in and its surface area is 90 in², we can set up a ratio of the surface areas of the two pyramids:
Surface area of the first pyramid / Surface area of the second pyramid = (Height of the first pyramid / Height of the second pyramid)²
Let's solve for the surface area of the second pyramid:
Surface area of the second pyramid = Surface area of the first pyramid × (Height of the second pyramid / Height of the first pyramid)²
Surface area of the second pyramid = 90 in² × (10 in / 5 in)²
Surface area of the second pyramid = 90 in² × (2)²
Surface area of the second pyramid = 90 in² × 4
Surface area of the second pyramid = 360 in²
Therefore, the surface area of a similar pyramid with a height of 10 inches is 360 square inches.
To find the surface area of a similar pyramid with a height of 10 in, we need to use the concept of similarity.
Similar shapes have proportional side lengths, which means that if we double one side length, we also double the corresponding side length in the similar shape.
In this case, if the height of the first pyramid is 5 in and the surface area is 90 in², we can express the ratio of their heights as:
height1 : height2 = 5 in : 10 in
To find the ratio of their surface areas, we need to square the ratio of their heights:
(ratio of surface areas)² = (height2 ÷ height1)²
Plugging in the values:
(ratio of surface areas)² = (10 in ÷ 5 in)²
= 2²
= 4
From the equation, we get that the ratio of surface areas is 2.
To find the surface area of the similar pyramid with a height of 10 in, multiply the surface area of the original pyramid by the ratio of surface areas:
surface area2 = surface area1 × (ratio of surface areas)
= 90 in² × 2
= 180 in²
Therefore, the surface area of the similar pyramid with a height of 10 in is 180 square inches.