Edge Lengths Find the volume of each right rectangular prism. The answers are mixed up at the bottom of the page Cross out the answers as you complete the problems. t=1cm 1=2(1)/(2)cm w=(1)/(3)cm h=3 cm w=(1)/(2)cm h=2cm __ __ I=(2)/(3)cm (4) 1=6 cm w=3cm h=4(1)/(3)cm w=(2)/(3) cm h=(3)/(4) cm __ __ l=5(1)/(3)cm (a) =8(1)/(4) cm w=(4)/(5)cm h=(1)/(3)cm __ __ ) I=2(1)/(2) cm (8) I=1(1)/(3)cm w=1(1)/(2)cm h=3(1)/(2)cm w=(1)/(2) cm h=6(1)/(5)cm

Para encontrar el volumen de un prisma rectangular, se utiliza la fórmula:<br /><br />\[ V = l \times w \times h \]<br /><br />Donde:<br />- \( l \) es la longitud<br />- \( w \) es el ancho<br />- \( h \) es la altura<br /><br />Vamos a calcular el volumen de cada prisma rectangular:<br /><br />1. Para el primer prisma:<br /> - \( l = 2\frac{1}{2} \) cm<br /> - \( w = \frac{1}{3} \) cm<br /> - \( h = 3 \) cm<br /><br /> \[ V = 2\frac{1}{2} \times \frac{1}{3} \times 3 = \frac{5}{2} \times \frac{1}{3} \times 3 = \frac{5}{2} \times 1 = \frac{5}{2} \, \text{cm}^3 \]<br /><br />2. Para el segundo prisma:<br /> - \( l = \frac{2}{3} \) cm<br /> - \( w = \frac{1}{2} \) cm<br /> - \( h = 2 \) cm<br /><br /> \[ V = \frac{2}{3} \times \frac{1}{2} \times 2 = \frac{2}{3} \times 1 = \frac{2}{3} \, \text{cm}^3 \]<br /><br />3. Para el tercer prisma:<br /> - \( l = 6 \) cm<br /> - \( w = 3 \) cm<br /> - \( h = 4\frac{1}{3} \) cm<br /><br /> \[ V = 6 \times 3 \times 4\frac{1}{3} = 6 \times 3 \times \frac{13}{3} = 6 \times 13 = 78 \, \text{cm}^3 \]<br /><br />4. Para el cuarto prisma:<br /> - \( l = 8\frac{1}{4} \) cm<br /> - \( w = \frac{4}{5} \) cm<br /> - \( h = \frac{1}{3} \) cm<br /><br /> \[ V = 8\frac{1}{4} \times \frac{4}{5} \times \frac{1}{3} = \frac{33}{4} \times \frac{4}{5} \times \frac{1}{3} = \frac{33}{4} \times \frac{4}{15} = \frac{33}{15} = 2.2 \, \text{cm}^3 \]<br /><br />5. Para el quinto prisma:<br /> - \( l = 2\1}{2} \) cm<br /> - \( w = 1\frac{1}{2} \) cm<br /> - \( h = 3\frac{1}{2} \) cm<br /><br /> \[ V = 2\frac{1}{2} \times 1\frac{1}{2} \times 3\frac{1}{2} = \frac{5}{2} \times \frac{3}{2} \times \frac{7}{2} = \frac{5 \times 3 \times 7}{4} = \frac{105}{4} = 26.25 \, \text{cm}^3 \]<br /><br />6. Para el sexto prisma:<br /> - \( l = 1\frac{1}{3} \) cm<br /> - \( w = \frac{1}{2} \) cm<br /> - \( h = 6\frac{1}{5} \) cm<br /><br /> \[ V = 1\frac{1}{3} \times \frac{1}{2} \times 6\frac{1}{5} = \frac{4}{3} \times \frac{1}{2} \times \frac{31}{5} = \frac{4}{3} \times \frac{31}{10} = \frac{4 \times 31}{3 \times 10} = \frac{124}{30} = 4.13 \, \text{cm}^3 \]<br /><br />Por lo tanto, los volúmenes de los prismas rectangulares son:<br />1. \( \frac{5}{2} \, \text{cm}^3 \)<br />2. \( \frac{2}{3} \, \text{cm}^3 \)<br />3. \( 78 \, \text{cm}^3 \)<br />4. \( 2.2 \, \text{cm}^3 \)<br />5. \( 26.25 \