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
<h3>What is scale factor?</h3>
Scale factor is the ratio of two similar quantities
<h3>a. How to find the volume of Prism 1.</h3>
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
<h3>b. How to find the surface area of the white eraser?.</h3>
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:
brainly.com/question/26161002
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