Question

El área lateral de un cono es 188,4 cm2 y el area total es 301,44 cm2 .¿ Cuánto es el volumen del cono ? Observación utilizar pi=3,14.​

Answer 1

Respuesta:

 

 $V = 301.44cm^{3}$

Explicación paso a paso:

Area Lateral: $A_{L} = 188.4 cm^{2}$

Area Total: $A_{t} = 301.44cm^{2}$

$\pi = 3.14$

$V= ?$

Area de la base:

$A_{B} = \pi r^{2}$

Area Lateral:

$A_{L} = \pi rg$

Area Total:

$A_{t} = \pi rg + \pi r^{2}$

$301.44cm^{2} = 188.4cm^{2} + \pi r^{2}$

$301.44cm^{2} - 188.4cm^{2} = (3.14) r^{2}$

$113.04 cm^{2} = (3.14)r^{2}$

$\frac{113.04cm^{2} }{3.14} = r^{2}$

$36cm^{2} = r^{2}$

$\sqrt{36cm^{2} } = r$

$6cm = r$

$A_{L} = \pi rg$

$188.4cm^{2} = (3.14)( 6cm )g$

$188.4cm^{2} = 18.84cm (g)$

$\frac{188.4cm^{2} }{18.84cm} = g$

$10cm = g$

$h = \sqrt{g^{2}-r^{2} } = \sqrt{10^{2}-6^{2} } = \sqrt{100-36} = \sqrt{64cm^{2} } =8cm$

$Volumen:$

$V =\frac{\pi r^{2}h }{3} = \frac{(3.14)(6cm)^{2}(8cm) }{3} = \frac{(3.14)(36)(8)cm^{3} }{3}= \frac{904.32cm^{3} }{3}$

$V = 301.44cm^{3}$