Question

If the surface area of a sphere is 616 cm
find its diameter.​

Answer 1

GiveN:-

Surface area of sphere is 616 cm².

To FinD:-

Its diameter.

SolutioN:-

We know that,

$\large{\green{\underline{\boxed{\bf{Surface\:Area=4\pi\:r^2}}}}}$

where,

• Surface Area = 616 cm²
• π = 22/7
• r is radius = ?

Putting the values,

$\large\implies{\sf{616=4\times\dfrac{22}{7}\times\:r^2}}$

$\large\implies{\sf{616=\dfrac{88}{7}\times\:r^2}}$

$\large\implies{\sf{\dfrac{616\times7}{88}=r^2}}$

$\large\implies{\sf{\dfrac{4312}{88}=r^2}}$

$\large\implies{\sf{\dfrac{\cancel{4312}}{\cancel{88}}=r^2}}$

$\large\implies{\sf{49=r^2}}$

Square rooting both the sides,

$\large\implies{\sf{\sqrt{49}=r}}$

$\large\implies{\sf{7=r}}$

$\large\therefore\boxed{\bf{Radius=7\:cm.}}$

Now the diameter:-

$\large{\green{\underline{\boxed{\bf{Diameter=2\times\:radius}}}}}$

where,

• Radius = 7 cm.

Putting the values,

$\large\implies{\sf{Diameter=2\times7}}$

$\large\therefore\boxed{\bf{Diameter=14\:cm.}}$

The diameter of the sphere is 14 cm.