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PRISMA Y CILINDROPROBLEMA 19SeaABC-DEFun prisma oblicuo de altura BF. Calcule

el volumen del solido.

RESOLUCIONAl ser un prisma oblicuo de altura BF entonces la arista

BF es perpendicular a las aristas EF y DF.En el triangulo DEF aplicamos el teorema de Pitgoras:Entonces EF=3.En el triangulo notable EBF, BF=4.

Calculando el volumen:

Por lo tanto .

PROBLEMA 20Se tiene un prisma regular triangular ABC-DEF, sus

caras laterales son regiones cuadradas, cuyas reas son

numricamente iguales al permetro de las bases. Halle

el volumen de dicho prisma.

RESOLUCION Por dato, el rea de una cara lateral (regin cuadrada) es

numricamente igual al permetro de la base, entonces, entonces .

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Calculando el volumen Por lo tanto.

PROBLEMA 21Del grafico, ABCD-EFGH y CPQR-GSTO son prismas

regulares cuya suma de volmenes es 5. Si DM=2(MR),

calcule el volumen del prisma ARQD-EOTH.

RESOLUCION

Por dato , entonces

.Piden; Pero

.Por lo tanto .En el grafico se muestra al solido visto desde la partesuperior:

PROBLEMA 22Si un cilindro equiltero tiene volumen 16, calcule e

rea de la superficie total.RESOLUCIONSi un cilindro es equiltero entonces la longitud de la

generatriz es igual al dimetro de la su base.Por dato entonces .

Piden Por lo tanto .

PROBLEMA 23Sea CD la generatriz de un cilindro circular recto y O e

centro de una de sus bases. Si y

entonces, Cul es el rea lateral (en ) del cilindro?

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RESOLUCIONAl graficar se forma el triangulo OCD notable de 15,

75 entonces se cumple que la hipotenusa de longitud 8

es cuatro veces su altura relativa.Nos pidenPero por relaciones mtricas Por lo tanto .

PROBLEMA 24Del grafico, se muestra un cilindro de revolucin lleno

de agua y dentro de el un cubo, calcule el volumen de

agua que hay en el cilindro.RESOLUCIONEl agua debe ser el volumen del cilindro menos el

volumen del cuboPor lo tanto .

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