Q. 1 If the perimeter of a protractor is 72 𝑐𝑚, calculate its area. (Use π =22/7).

 

(OR)

 

Q.2 If the total surface area of a solid hemisphere is 462 cm², find its volume. [Take π = 22/7]

It is given that the perimeter of a protractor is 72 𝑐𝑚 and we need to find its area.

 It is known that the protractor in the semi-circular form and for a semi-circular solid, the
perimeter (𝑃) and the area (𝐴) is given by 𝑃 = (π + 2)𝑟 and 𝐴 = π𝑟²/2 where 𝑟 is the radius of the solid. 

Therefore, on substituting the values in the perimeter formula, we get
𝑃 = π𝑟
⇒ 72 = (π + 2)𝑟
   r = 72 /(π+2)
⇒ 𝑟 = 14 𝑐𝑚
Now, the area can be calculated as

A = π𝑟²/2

A=  π(14)²/2
⇒ 𝐴 = 196π/2
⇒ 𝐴 = 308 𝑐𝑚²
Hence, the area of the protractor is 308 cm²

^(OR)

We need to find the volume if the total surface area of a solid hemisphere is

462 𝑐𝑚² .

It is known that the TSA of hemisphere is given by 𝑇𝑆𝐴 = 3π𝑟², where 𝑟 is the radius of the hemisphere.

On substituting the given value of TSA, we get

⇒ 𝑇𝑆𝐴 = 3π𝑟²

⇒ 462 = 3π𝑟²

⇒ 154 = π𝑟²

⇒ 49 = 𝑟²
⇒ 𝑟 = 7 𝑐𝑚
Now, the volume of the hemisphere is given by 𝑉 = 2/3 π𝑟³.
On substituting the values, we get the volume as
𝑉 = 2/3 π𝑟³
⇒ 𝑉 = 2/3 x 22/7 x 7³
⇒ 𝑉 = 718. 67 𝑐𝑚³
Hence, the volume of the hemisphere 718.67 cm³