Answer :
The box measures 32 Centimeters by 19 centimeters by 14 centimeters, with a volume of 8,192 cubic centimeters, a surface area of 2,644 square centimeters, and a diagonal of approximately 39.77 centimeters.
The dimensions of the box are given as follows:
Length = 32 centimeters
Width = 19 centimeters
Height = 14 centimeters
These dimensions represent the measurements of the box in three orthogonal directions. The length refers to the longest side of the box, the width represents the side perpendicular to the length, and the height is the vertical dimension.
Using these dimensions, we can calculate certain properties of the box:
1. Volume:
The volume of the box can be found by multiplying the length, width, and height together:
Volume = Length x Width x Height = 32 cm x 19 cm x 14 cm = 8,192 cubic centimeters.
2. Surface Area:
The surface area of the box can be determined by calculating the area of each of its six sides and summing them up. Since the box has a rectangular shape, each side can be treated as a rectangle.
Surface Area = 2lw + 2lh + 2wh
= 2(32 cm x 19 cm) + 2(32 cm x 14 cm) + 2(19 cm x 14 cm)
= 1,216 cm² + 896 cm² + 532 cm²
= 2,644 cm².
3. Diagonal:
The diagonal of the box can be found using the Pythagorean theorem. We can consider the length, width, and height as the three sides of a right-angled triangle.
Diagonal = √(Length² + Width² + Height²)
= √(32 cm)² + (19 cm)² + (14 cm)²
= √1,024 cm² + 361 cm² + 196 cm²
= √1,581 cm²
≈ 39.77 cm.
Therefore, the box measures 32 centimeters by 19 centimeters by 14 centimeters, with a volume of 8,192 cubic centimeters, a surface area of 2,644 square centimeters, and a diagonal of approximately 39.77 centimeters.
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