Answer:
76.5 cm²
Step-by-step explanation:
Given the triangles are similar , then
ratio of sides = a : b , so
ratio of areas = a² : b²
Here ratio of sides = 9 : 13.5 = 2 : 3
ratio of areas = 2² : 3² = 4 : 9
let x be the area of Δ DEF and using proportion
=
( cross- multiply )
4x = 306 ( divide both sides by 4 )
x = 76.5
The area of Δ DEF = 76.5 cm²
The surface area of the larger solid, rounded to the nearest hundredth is given by: Option B:
Volume of a solid is usually expressed in cubic units, or units cube.
Suppose that the volume was expressed in x cubic units. Then you can say that the considered solid takes same space as the volume occupied by x cubes of 1 unit as their side lengths.
<h3>What are similar objects?</h3>They're like zoomed version of each other(might be non-zoomed, zoomed in, or zoomed out). Their sides can be obtained by multiplying one object's sides by a single constant(by single constant, we mean constant which will be same for obtaining any corresponding side).
For the given case, we're given that:
Both solids are similar.
Thus, let the scale factor by which their sides change be 'f'.
Then, we get:
(as two times sides multiplied, so two times f got multiplied).
Similarly,
Or
As surface area of smaller solid(second solid is smaller as its volume is less) is 74.32 sq. inches, and f = 1.8, thus, we get:
Thus, the surface area of the larger solid, rounded to the nearest hundredth is given by: Option B:
Learn more about volume and surface area here: