Question

A toy is in the form of a cone of radius 3.5m mounted on a hemisphere of same radius, the total height of a toy is 15.5cm. find the S.A of the toy. ​

Answer 1

GIVEN :

• A toy is in the form of a cone of radius 3.5m mounted on a hemisphere of same radius, the total height of a toy is 15.5 cm.

TO FIND :

• The total surface area of the toy = ?

SOLUTION :

Let the radius, height and slant height of the cone be the r cm, h cm and l cm respectively.

r = 3.5 cm

h = ( 15.5 - 3.5 ) = 12 cm

➨ l = $\sf \sqrt{(3.5)^{2} + (12)^{2}}$

➨ l = $\sf \sqrt{12.25 + 144}$

➨ l = $\sf \sqrt{156.25}$

➨ $\pink{\sf l =12.5 \:cm}$

So,

➨ TSA of the toy = 2πr² + πrl

➨ TSA of the toy = 2π(3.5)² + π(3.5)(12.5)

➨ TSA of the toy = 24.5π + 43.7π

➨ TSA of the toy = 68.25π

➨ TSA of the toy = 68.25 × 22/7

➨ TSA of the toy = 214.5 cm²

Therefore, TSA of toy is 214.5 cm².

Answer 2

SOLUTION :-

Radius of cone = Radius of hemisphere = 3.5cm

Height of conical part = 15.5 - 3.5 = 12cm

Slant height = √(r² + h²) = 15/2cm

Now,

C.S.A= C.S.A of conical part = C.s.a of hemisphere

C.S.A = πrl + 2πr²

C.S.A = 214.5 cm²