Question

The length of the longest diagonal of a cube is 25cm. Calculate the total surface area of the cube

Answer 1

Step-by-step explanation:

This is the required answer.

Feel free to ask any doubt.

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Yash Sharma

Answer 2

Concept:

A Cube is a 3-D object.six-sided solid form with six faces. One of the most basic shapes in three dimensions is the cube. A cube's six faces are all squares, making it a two-dimensional object.

The amount of space a cube can hold is measured by its volume. If an object has a cubic shape and we need to fill it with anything, let's say water, then the amount of water in litres that needs to be kept inside the object is determined by its volume. The volume formula is provided by:

Volume of cube = a³ cubic units

If a is the length of the side, then,

Length of Diagonal of Face of the Cube = √2 a

Length of Diagonal of Cube = √3 a

Total surface area = 6a²

Given:

The length of the longest diagonal of a cube is 25cm

Find:

Calculate the total surface area of the CUBE

Solution:

Length of the longest diagonal =√3 a

As per question,

√3a = 25

a= 25/√3

Total surface area of square = 6a²

                                                 = 6 x (25/√3)²

                                                 = 6 x 625/3

                                                  =1250 cm ²

Therefore, the total surface area of  the cube is 1250cm²

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