Question

If curved surface area of sphere is 154cm square then what will be the daimeter of sphere?

Answer 1

Given :-

• CSA of a sphere = 154 cm²

To Find :-

• Diameter of the sphere

Solution :-

$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$

$\star\: \boxed{\sf{\blue{CSA\;of\;sphere=4\pi r^{2} }}}$

→ Let's find out the radius of the sphere by putting values in this formula

$\sf \implies 154 = 4 \times \dfrac{22}{7} \times r^{2}$

$\sf \implies r^{2} = \dfrac{154 \times 7 }{4 \times 22}$

$\sf \implies r^{2} = \dfrac{1078}{88}$

$\sf \implies r = \sqrt{\dfrac{1078}{88} }$

$\sf \implies r = \sqrt{12.25}$

$\sf \implies r = 3.5$

→ ATQ  we need to find the diameter

$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$

$\star\: \boxed{\sf{\blue{Diameter = 2 \times Radius }}}$

$\sf Diameter = 2 \times 3.5$

$\sf \implies Diameter = 7 \; cm$

∴ Diameter of the sphere is 7 cm

Answer 2

Given :-

• Surface area of sphere = 154cm³

To find :-

• The diameter

Solution :-

Using the formula,

Surface area of sphere = 4 πr²

Where,

• r = radius
• surface area = 154cm³

Putting values,

⇛Surface area = 4πr²

⇛154 = 4 ( 22/7 )r²

⇛r² ( 154 x 7 ) / ( 4x 22 )

⇛r = 35/10

⇛r = 3.5cm

Using the formula,

Diameter = 2r

Putting values

⇛Diameter = 2r

⇛ 2 ( 3.5 )

⇛7cm

Therefore, the radius of the sphere is 7cm.