Questions: Find the total outside surface area and the volume of the solid.

Find the total outside surface area and the volume of the solid.
Transcript text: Find the total outside surface area and the volume of the solid.
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Solution

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△ Calculate the total outside surface area of the solid. ○ Calculate area of front and back faces ▷ Determine the area of the parallelogram-shaped front and back faces. ☼ The area of each face is \( 24 \, \text{cm} \times 14 \, \text{cm} = 336 \, \text{cm}^2 \). Since there are two such faces, the total area is \( 2 \times 336 \, \text{cm}^2 = 672 \, \text{cm}^2 \). ○ Calculate area of left and right faces ▷ Determine the area of the parallelogram-shaped left and right faces. ☼ The area of each face is \( 24 \, \text{cm} \times 26 \, \text{cm} = 624 \, \text{cm}^2 \). Since there are two such faces, the total area is \( 2 \times 624 \, \text{cm}^2 = 1248 \, \text{cm}^2 \). ○ Calculate area of top and bottom faces ▷ Determine the area of the parallelogram-shaped top and bottom faces. ☼ The area of each face is \( 25 \, \text{cm} \times 14 \, \text{cm} = 350 \, \text{cm}^2 \). Since there are two such faces, the total area is \( 2 \times 350 \, \text{cm}^2 = 700 \, \text{cm}^2 \). ○ Calculate total surface area ▷ Sum the areas of all faces to find the total surface area. ☼ The total surface area is \( 672 \, \text{cm}^2 + 1248 \, \text{cm}^2 + 700 \, \text{cm}^2 = 2620 \, \text{cm}^2 \). ✧ The total outside surface area is \( 2620 \, \text{cm}^2 \). △ Calculate the volume of the solid. ○ Calculate the volume ▷ Use the formula for the volume of a parallelepiped. ☼ The volume is calculated as \( 24 \, \text{cm} \times 25 \, \text{cm} \times 14 \, \text{cm} = 8400 \, \text{cm}^3 \). ✧ The volume of the solid is \( 8400 \, \text{cm}^3 \). ☺ Total outside surface area: 2620 cm² Volume: 8400 cm³

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