Question

If the total surface area of a hemi sphere is 1848 cm , then its diameter is

Answer 1

A N S W E R :

• Diameter or hemisphere is 28 cm.

G I V E N :

• Total Surface Area of hemisphere is 1848 cm².

T O F I N D :

• Diameter of hemisphere = ?

C O N C E P T :

• TSA of hemisphere = 3πr²
• Diameter = Radius × 2

S O L U T I O N :

• To calculate diameter of hemisphere first we have to calculate radius of hemisphere. Radius of hemisphere can be calculated by the given below process. After claculating the radius of hemisphere we can find the diameter of hemisphere :]

Let radius of hemisphere be 'r'

★ According to Question now :

→ TSA of hemisphere = 3πr²

→ 1848 cm² = 3πr²

→ 1848 ÷ 3 = πr²

→ 616 = πr²

→ 616 = 22/7 × r²

→ (616 × 7) ÷ 22 = r²

→ 4312 ÷ 22 = r²

→ 196 = r²

→ r² = 196

→ r = √196

→ r = 14 cm

Therefore,radius of hemisphere is 14 cm.

Finding diameter of cone :

➝ Diameter = Radius × 2

➝ Diameter = 14 × 2

➝ Diameter = 28 cm

Hence,the diameter of hemisphere is 28 cm.

Answer 2

$\huge\bold{\mathbb{QUESTION}}$

If the total surface area of a hemisphere is $1848\: cm,$ then its diameter is ?

$\huge\bold{\mathbb{GIVEN}}$

• The total surface area of a hemi sphere is $1848\: cm.$

$\huge\bold{\mathbb{TO\:FIND}}$

The length of its diameter.

$\huge\bold{\mathbb{SOLUTION}}$

Let the radius of the hemisphere be $r\:cm.$

We know that:

$\boxed{\large\sf{TSA_{(Hemisphere)}=3πr^2\:unit^2}}$

Let's find out the radius.

Putting the formula.

$3πr^2=1848$

$\implies 3\times{\dfrac{22}{7}}\times r^2=1848$

$\implies {\dfrac{(3\times22)}{7}}\times r^2=1848$

$\implies {\dfrac{66}{7}}\times r^2=1848$

$\implies r^2=1848\div {\dfrac{66}{7}}$

$\implies r^2=1848\times {\dfrac{7}{66}}$

$\implies r^2=\cancel{1848}\times {\dfrac{7}{\cancel{66}}}$

$\implies r^2=28\times 7$

$\implies r^2=196$

$\implies r= \sqrt{196}$

$\implies \boxed{\red{r=14}}$

So, radius $=r\:cm=14\:cm$

$\:$

We know that:

$\boxed{\large\sf{Diameter=2\times Radius}}$

Putting the formula.

$Diameter \,\,=2\times r$

$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \;=(2\times 14)\:cm$

$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \;= \boxed{\red{28\:cm}}$

$\huge\bold{\mathbb{THEREFORE}}$

The diameter of the hemisphere is $28\:cm.$

$\huge\bold{\mathbb{WE\:\,MADE\:\,IT\:\,!!}}$