Question

The end points of an edge of a cube are (0,0) and (4,0). Find lateral surface area of cube and length of
the diagonal of its face.​

Answer 1

Step-by-step explanation:

Given:-

The end points of an edge of a cube are (0,0) and (4,0).

To find:-

Find lateral surface area of cube and length of the diagonal of its face.

Solution:-

The end points of an edge of a cube are (0,0) and (4,0)

Let (x,y)=(4,0)=>x=4;y=0

(0,0)= The origin

The distance from the origin to the point (x,y) is √(x²+y²) units

=>√(0²+4²)

=>√(0+16)

=>√16

=>4 units

The distance is 4 units

The length of the edge of the cube = 4 units

1)Lateral surface area of a cube :-

The edge of a cube is "a" units then the lateral surface area of a cube is 4a² sq.units

we have a= 4 units

Lateral surface area = 4(4²)

=>4×4×4

=>64 sq.units

Lateral surface area of the cube = 64 sq.units

2)Length of the diagonal of the face:-

The edge of a cube is "a" units then the length of the diagonal is √3× length of the side=√3 a units

=>Diagonal =4(√3) units

Length of the diagonal = 4√3 units

Answer:-

1) Lateral surface area of the cube = 64 sq.units

2) Length of the diagonal of the face of the cube = 4√3 units

Used formulae:-

The edge of a cube is "a" units then ,

• Lateral surface area = 4a² sq.units
• Length of the diagonal = √3 a units

The distance between the origin (0,0) and the point (x,y) is √(x²+y²) units