Respuesta :
Answer:
[tex]\large\boxed{V_A=1512\ m^3}[/tex]
Step-by-step explanation:
[tex]\text{If a prism A is similar to a prism B with a scale k, then:}\\\\\text{1.\ The ratio of the lengths of the corresponding edges is equal to the scale k}\\\\\dfrac{a}{b}=k\\\\\text{2. The ratio of the surface area of the prisms is equal}\\\text{to the square of the scale k}\\\\\dfrac{S.A._A}{S.A._B}=k^2\\\\\text{3. The ratio of the prism volume is equal to the cube of the scale k}\\\\\dfrac{V_A}{V_B}=k^3[/tex]
[tex]\text{We have}\\\\k=6:5=\dfrac{6}{5}\\\\V_B=875\ m^3\\\\V_A=x\\\\\text{Substitute to 3.}\\\\\dfrac{x}{875}=\left(\dfrac{6}{5}\right)^3\\\\\dfrac{x}{875}=\dfrac{216}{125}\qquad\text{cross multiply}\\\\125x=(875)(216)\qquad\text{divide both sides by 125}\\\\x=\dfrac{(875)(216)}{125}\\\\x=\dfrac{(7)(216)}{1}\\\\x=1512\ m^3[/tex]
Prism A is similar to Prism B with a scale factor of 6:5. If the volume of Prism B is 875 m2. The volume of prism B is 1512 meter square.
How to calculate the scale factor?
Suppose the initial measurement of a figure was x units.
And let the figure is scaled and the new measurement is of y units.
Since the scaling is done by multiplication of some constant, that constant is called the scale factor.
Let that constant be 's'.
Then we have:
[tex]s \times x = y\\s = \dfrac{y}{x}[/tex]
Thus, the scale factor is the ratio of the new measurement to the old measurement.
Prism A is similar to Prism B with a scale factor of 6:5.
If the volume of Prism B is 875 m2, find the volume of Prism A.
scale factor = 6/5
The ratio of the surface area of the prism A to the prism B
A1 / A2 = k^2
The ratio of the prism is equal to the cube of the scale k.
V1 / V2 = k^3
Let x be the volume of Prism A.
x / 875 = (6/5)^2
x / 875 = 216 / 125
x = 875 * 216 / 125
x = 1512
Therefore, the volume of prism B is 1512 meter square.
learn more on scale factors here:
brainly.com/question/14967117
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