a. The volume of prism 1 is 8346.562 ft³
b. The surface area of the white eraser is 13 cm²
The question has to do with scale factor
What is scale factor?
Scale factor is the ratio of two similar quantities
a. How to find the volume of Prism 1.
Since
- Prism 1 has a surface area of A = 289 ft² and
- Prism 2 has a surface area of A' = 529 ft².
Let
- L be the length of side of prism 1 and
- L' the length of side of prism 2
We have that scale factor = A/A'
Also,
A/A' = (L/L')²
L/L = √(A/A') = √( 289 ft²/ 529 ft²) = √0.49 = 0.7
Since
- prism 1 has a volume of V and
- prism 2 has a volume of V' = 24334 ft³. We have that
V/V' = (L/L')³
So, V = (L/L')³V'
So, substituting the values of the variables into the equation, we have
V = (L/L')³V'
V = (0.7)³24334 ft³
V = 0.343 × 24334 ft³
V = 8346.562 ft³
So, the volume of prism 1 is 8346.562 ft³
b. How to find the surface area of the white eraser?.
Since
- The white eraser has volume of V = 2 cm³ and
- The yellow eraser has volume of V' = 16 cm³.
Let
- L be the length of side of white eraser and
- L' the length of side of yellow eraser
We have that scale factor = V/V'
Also, V/V' = (L/L')³
L/L = ∛(V/V')
= ∛( 2 cm³/16 cm³)
= ∛(1/8)
= 1/2
Since
- White eraser has a surface area of A and
- Yellow eraser has a surface area of A = 52 cm² . We have that
A/A' = (L/L')²
So, A = (L/L')²A'
So, substituting the values of the variables into the equation, we have
A = (L/L')²A'
A = (1/2)²52 cm²
A = 1/4 × 52 cm²
A = 13 cm²
So, the surface area of the white eraser is 13 cm²
Learn more about scale factor and surface area here:
https://brainly.com/question/26161002
#SPJ1
