Question

Find the surface area of the largest possible cube model out of the wooden sphere radius 5 root3

Answer 1

radius of the wooden sphere=5√3
diameter=2×5√3=10√3.
now,
diagonal of the cube=diameter of the wooden sphere.
√3a=10√3
a=10√3/√3
a=10.

surface area of the cube=6a^2
=6×(10)^2
=6×100
=600.
therefore, the surface area of the largest cube that can be made out of a wooden sphere of radius 5√3 is 600.

Answer 2

Given :
radius of sphere (r) = 5√3

Required to find :
surface area of the largest possible cube made out of a wooden sphere of radius 5√3.

Solution :
• let the side of cube is 'a'
then the diagonal of the cube is given by a√3

• the diagonal of the largest possible cube made out of a sphere coincides with the diameter of the sphere.

given that,
radius of sphere = 5√3
diameter of sphere = 10√3
→ diagonal of cube = 10√3
a√3 = 10√3
a = 10

the total surface area of the cube is given by 6a^2.
surface area
= 6 × 10^2
= 6 × 100
= 600

RESULT :
the surface area of the largest possible cube made out of a wooden sphere of radius 6√3 is 600 sq.units