A cuboid has a length 13cm,with 9cm and height 8cm.calculate the surface area, length of it's diagonal and volume
To calculate the surface area of a cuboid, you need to calculate the areas of all six faces and sum them up. The formula for the surface area of a cuboid is:
Surface Area = 2(length × width + length × height + width × height)
Let's substitute the given values into the formula:
Length = 13 cm
Width = 9 cm
Height = 8 cm
Surface Area = 2(13 × 9 + 13 × 8 + 9 × 8)
= 2(117 + 104 + 72)
= 2(293)
= 586 cm²
Therefore, the surface area of the cuboid is 586 cm².
To calculate the length of the diagonal of a cuboid, you can use the Pythagorean theorem. The formula for finding the diagonal is:
Diagonal = √(length² + width² + height²)
Substituting the given values:
Length = 13 cm
Width = 9 cm
Height = 8 cm
Diagonal = √(13² + 9² + 8²)
= √(169 + 81 + 64)
= √(314)
= 17.72 cm (rounded to two decimal places)
Therefore, the length of the diagonal of the cuboid is approximately 17.72 cm.
To calculate the volume of a cuboid, you simply multiply its dimensions. The formula for the volume of a cuboid is:
Volume = length × width × height
Substituting the given values:
Length = 13 cm
Width = 9 cm
Height = 8 cm
Volume = 13 × 9 × 8
= 936 cm³
Therefore, the volume of the cuboid is 936 cm³.