Respuestas
Respuesta dada por:
2
¡Hola!
Vamos a encontrar los volúmenes de las siguientes figuras:
1) cilindro + cono
2) cubo
3) cuadrilátero
4) esfera
Resolviendo:
Si: π ≈ 3,14
1) volumen de (cilindro + cono)
![V{cilindro} = \pi *r^2*h V{cilindro} = \pi *r^2*h](https://tex.z-dn.net/?f=V%7Bcilindro%7D+%3D++%5Cpi+%2Ar%5E2%2Ah)
![V_{cilindro} = \pi *2^2*3 V_{cilindro} = \pi *2^2*3](https://tex.z-dn.net/?f=V_%7Bcilindro%7D+%3D++%5Cpi+%2A2%5E2%2A3)
![V_{cilindro} = \pi *4*3 V_{cilindro} = \pi *4*3](https://tex.z-dn.net/?f=V_%7Bcilindro%7D+%3D++%5Cpi+%2A4%2A3)
![V_{cilindro} = 12\pi V_{cilindro} = 12\pi](https://tex.z-dn.net/?f=V_%7Bcilindro%7D+%3D+12%5Cpi)
![V_{cilindro} = 12*3,14 V_{cilindro} = 12*3,14](https://tex.z-dn.net/?f=V_%7Bcilindro%7D+%3D+12%2A3%2C14)
![\boxed{V_{cilindro} = 37,68\:cm^3} \boxed{V_{cilindro} = 37,68\:cm^3}](https://tex.z-dn.net/?f=%5Cboxed%7BV_%7Bcilindro%7D+%3D+37%2C68%5C%3Acm%5E3%7D)
y
![V_{cone} = \frac{ \pi*r^2*h}{3} V_{cone} = \frac{ \pi*r^2*h}{3}](https://tex.z-dn.net/?f=V_%7Bcone%7D+%3D++%5Cfrac%7B+%5Cpi%2Ar%5E2%2Ah%7D%7B3%7D+)
![V_{cone} = \frac{ \pi*2^2*2,5}{3} V_{cone} = \frac{ \pi*2^2*2,5}{3}](https://tex.z-dn.net/?f=V_%7Bcone%7D+%3D+%5Cfrac%7B+%5Cpi%2A2%5E2%2A2%2C5%7D%7B3%7D+)
![V_{cone} = \frac{ \pi*4*2,5}{3} V_{cone} = \frac{ \pi*4*2,5}{3}](https://tex.z-dn.net/?f=V_%7Bcone%7D+%3D+%5Cfrac%7B+%5Cpi%2A4%2A2%2C5%7D%7B3%7D+)
![V_{cone} = \frac{10\pi}{3} V_{cone} = \frac{10\pi}{3}](https://tex.z-dn.net/?f=V_%7Bcone%7D+%3D+%5Cfrac%7B10%5Cpi%7D%7B3%7D)
![V_{cone} = \frac{10*3,14}{3} V_{cone} = \frac{10*3,14}{3}](https://tex.z-dn.net/?f=V_%7Bcone%7D+%3D+%5Cfrac%7B10%2A3%2C14%7D%7B3%7D+)
![V_{cone} = \frac{31,4}{3} V_{cone} = \frac{31,4}{3}](https://tex.z-dn.net/?f=V_%7Bcone%7D+%3D+%5Cfrac%7B31%2C4%7D%7B3%7D)
![\boxed{V_{cone} \approx 10,46\:cm^3} \boxed{V_{cone} \approx 10,46\:cm^3}](https://tex.z-dn.net/?f=%5Cboxed%7BV_%7Bcone%7D+%5Capprox+10%2C46%5C%3Acm%5E3%7D)
Por lo tanto:
![V_{cilindro} + V{cone} = 37,68 + 10,46 = \boxed{\boxed{48,14\:cm^3}}\end{array}}\qquad\checkmark V_{cilindro} + V{cone} = 37,68 + 10,46 = \boxed{\boxed{48,14\:cm^3}}\end{array}}\qquad\checkmark](https://tex.z-dn.net/?f=V_%7Bcilindro%7D+%2B+V%7Bcone%7D+%3D+37%2C68+%2B+10%2C46+%3D+%5Cboxed%7B%5Cboxed%7B48%2C14%5C%3Acm%5E3%7D%7D%5Cend%7Barray%7D%7D%5Cqquad%5Ccheckmark+)
2) Volumen del cubo
![V_{cubo} = a^3 V_{cubo} = a^3](https://tex.z-dn.net/?f=V_%7Bcubo%7D+%3D+a%5E3+)
![V_{cubo} = 4^3 V_{cubo} = 4^3](https://tex.z-dn.net/?f=V_%7Bcubo%7D+%3D+4%5E3)
![\boxed{\boxed{V_{cubo} = 64\:m^3}}\end{array}}\qquad\checkmark \boxed{\boxed{V_{cubo} = 64\:m^3}}\end{array}}\qquad\checkmark](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cboxed%7BV_%7Bcubo%7D+%3D+64%5C%3Am%5E3%7D%7D%5Cend%7Barray%7D%7D%5Cqquad%5Ccheckmark)
3) volumen del cuadrilátero
![V_{cuadrila\´tero} = a*b*c V_{cuadrila\´tero} = a*b*c](https://tex.z-dn.net/?f=V_%7Bcuadrila%5C%C2%B4tero%7D+%3D+a%2Ab%2Ac)
![V_{cuadrila\´tero} = 2,6*4,5*3,2 V_{cuadrila\´tero} = 2,6*4,5*3,2](https://tex.z-dn.net/?f=V_%7Bcuadrila%5C%C2%B4tero%7D+%3D+2%2C6%2A4%2C5%2A3%2C2)
![\boxed{\boxed{V_{cuadrila\´tero} = 37,44\:m^3}}\end{array}}\qquad\checkmark \boxed{\boxed{V_{cuadrila\´tero} = 37,44\:m^3}}\end{array}}\qquad\checkmark](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cboxed%7BV_%7Bcuadrila%5C%C2%B4tero%7D+%3D+37%2C44%5C%3Am%5E3%7D%7D%5Cend%7Barray%7D%7D%5Cqquad%5Ccheckmark)
4) volumen de la esfera
![V_{esfera} = \frac{4}{3} \pi*r^3 V_{esfera} = \frac{4}{3} \pi*r^3](https://tex.z-dn.net/?f=V_%7Besfera%7D+%3D++%5Cfrac%7B4%7D%7B3%7D+%5Cpi%2Ar%5E3)
![V_{esfera} = \frac{4}{3} *3,14*(3,92)^3 V_{esfera} = \frac{4}{3} *3,14*(3,92)^3](https://tex.z-dn.net/?f=V_%7Besfera%7D+%3D+%5Cfrac%7B4%7D%7B3%7D+%2A3%2C14%2A%283%2C92%29%5E3)
![V_{esfera} = \frac{4}{3} *3,14*60,236288 V_{esfera} = \frac{4}{3} *3,14*60,236288](https://tex.z-dn.net/?f=V_%7Besfera%7D+%3D+%5Cfrac%7B4%7D%7B3%7D+%2A3%2C14%2A60%2C236288)
![V_{esfera} = \frac{756,5677773}{3} V_{esfera} = \frac{756,5677773}{3}](https://tex.z-dn.net/?f=V_%7Besfera%7D+%3D+%5Cfrac%7B756%2C5677773%7D%7B3%7D)
![V_{esfera} = 252,18925991...\to \boxed{\boxed{V_{esfera} \approx 252,19\:cm^3}}\end{array}}\qquad\checkmark V_{esfera} = 252,18925991...\to \boxed{\boxed{V_{esfera} \approx 252,19\:cm^3}}\end{array}}\qquad\checkmark](https://tex.z-dn.net/?f=V_%7Besfera%7D+%3D+252%2C18925991...%5Cto+%5Cboxed%7B%5Cboxed%7BV_%7Besfera%7D+%5Capprox+252%2C19%5C%3Acm%5E3%7D%7D%5Cend%7Barray%7D%7D%5Cqquad%5Ccheckmark)
Vamos a encontrar los volúmenes de las siguientes figuras:
1) cilindro + cono
2) cubo
3) cuadrilátero
4) esfera
Resolviendo:
Si: π ≈ 3,14
1) volumen de (cilindro + cono)
y
Por lo tanto:
2) Volumen del cubo
3) volumen del cuadrilátero
4) volumen de la esfera
Preguntas similares
hace 6 años
hace 6 años
hace 9 años
hace 9 años
hace 9 años