Final answer:
The internal height of the cooler is approximately 28.6 cm. The internal surface area of the cooler is approximately 6,634 cm².
Step-by-step explanation:
To determine the internal height of the cooler, we need to find the height of the rectangular solid that represents the cooler's interior. We can use the formula for the volume of a rectangular solid: V = lwh, where l is the length, w is the width, and h is the height. In this case, the volume is 60 L, which is equivalent to 60,000 cm³.
The length is 60 cm and the width is 35 cm. Plugging these values into the volume formula, we can solve for the height:
V = 60,000 cm³ = (60 cm)(35 cm)(h) => h = 60,000 cm³ / (60 cm)(35 cm) = 28.6 cm
Therefore, the internal height of the cooler is approximately 28.6 cm.
To find the internal surface area, we need to calculate the area of each face of the rectangular solid and then sum them up. The area of each face is given by the formula A = lw, where l is the length and w is the width. There are 6 faces in total: 2 sides, 2 ends, a top, and a bottom. Plugging in the values, we can calculate the area for each face:
Area of a side = (60 cm)(28.6 cm) = 1,716 cm²
Area of an end = (35 cm)(28.6 cm) = 1,001 cm²
Area of top = (60 cm)(35 cm) = 2,100 cm²
Area of bottom = (60 cm)(35 cm) = 2,100 cm²
Summing up the areas of all the faces, we get:
Internal surface area = 2(1,716 cm²) + 2(1,001 cm²) + 2(2,100 cm²) = 3,432 cm² + 2,002 cm² + 4,200 cm² = 6,634 cm²
Therefore, the internal surface area of the cooler is approximately 6,634 cm².