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12345 [234]
2 years ago
5

En el estante de un negocio hay 2 tipos de tarros de la misma mermelada y marca. El tarro más alto tiene el doble de altura que

el otro, pero su diámetro es la mitad del diámetro del otro. El tarro más alto vale $4.500 y el más bajo $8.000, ¿ cuál es la mejor compra ? help
Mathematics
1 answer:
Ipatiy [6.2K]2 years ago
5 0

Answer:

tarro corto

Step-by-step explanation:

Aquí tenemos que comprar el frasco que tiene el menor costo por volumen.

h_1 = Altura del frasco corto

h_2 = La altura del frasco alto es el doble que el del frasco corto. = 2h_1

d_1 = Diámetro del frasco corto

d_2 = El diámetro del frasco alto es la mitad del frasco corto = \dfrac{1}{2}d_1

El volumen de un cilindro es \pi \dfrac{d^2}{4}h

La razón de los volúmenes de los frascos es

\dfrac{V_1}{V_2}=\dfrac{\pi\dfrac{d_1^2}{4}h_1}{\pi\dfrac{d_2^2}{4}h_2}\\\Rightarrow \dfrac{V_1}{V_2}=\dfrac{d_1^2h_1}{d_2^2h_2}\\\Rightarrow \dfrac{V_1}{V_2}=\dfrac{d_1^2h_1}{(\dfrac{1}{2}d_1)^22h_1}\\\Rightarrow \dfrac{V_1}{V_2}=\dfrac{d_1^2h_1}{\dfrac{1}{4}d_1^22h_1}\\\Rightarrow \dfrac{V_1}{V_2}=\dfrac{1}{\dfrac{1}{2}}\\\Rightarrow \dfrac{V_1}{V_2}=2\\\Rightarrow V_1=2V_2

El costo del frasco corto por unidad de volumen es

\dfrac{8000}{V_1}=\dfrac{8000}{2V_2}=\dfrac{4000}{V_2}

El costo del frasco alto por unidad de volumen es

\dfrac{4500}{V_2}=\dfrac{4500}{V_2}

\dfrac{4000}{V_2}

Entonces, el costo del frasco corto por unidad de volumen es menor que el costo por unidad de volumen del frasco alto.

Por lo tanto, deberíamos tomar el frasco corto.

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