Question

Rasheed got a playing top(lattu) as his birthday present which surprisingly had no colour on it. he want to colour it with caryons .the top is shaped like a cone surmounted by a hemisphere the entire top is 5 cm in height and the diameter of top is 3.5cm find the area he has to colour? π=22/7

Answer 1

Answer:

The net area he has to color is 38.95 cm²

Step-by-step explanation:

Given diameter of the top = 3.5 cm

=> diameter of hemisphere = diameter of cone = 3.5 cm

=> radius = 3.5/2 cm

Also

the total height of the top = radius of the hemisphere + height of cone

=> 5 = 3.5/2 + h

=> h = 5 - 3.5/2 = 6.5/2

surface area of hemisphere = 2πr²

= 2 x 22/7 x (3.5/2)²

= 19.25 cm²

surface area of cone = πr√(r² + h²)

= 22/7 x 3.5/2 x √[(3.5/2)² + (6.5/2)²]

= 22/7 x 3.5/2 x 3.58

= 19.7 cm²

Hence net surface area = 19.25 + 19.7 = 38.95 cm²

So the net area he has to color is 38.95 cm²

Answer 2

$\sf\huge\mathbb{Explanation:}$

Given that:-

• Rasheed got a playing top(lattu) as his birthday present which surprisingly had no colour on it.

• The top is shaped like a cone surmounted by a hemisphere the entire top is 5 cm in height.

• Diameter of the top = 3.5cm

To find:-

• The area he has to colour

____________________________________

( we have to take =π=22/7)

TSA of the toy = CSA of hemisphere + CSA of cone

Curved surface area of the hemisphere

= 1/ 2 (4πr^2) = 2π r^2 

= 2(22/7)× (3.5/2) × (3.5/2) cm^2

Height of the cone = Height of the top – Radius of the hemispherical part

= (5 – 3.5/2) cm = 3.25 cm

Sant height of the cone (l) 

=$\tt\bold{\sqrt{r^2+h^2}=\sqrt{(\frac{3.5}{2})^2+(3.25)^2}}$

=3.7cm ( approximate)

Therefore, CSA of cone = πrl = (22/7) × (3.5/2) × 3.7 cm^2

Hence, the surface area of the top = [2(22/7)× (3.5/2) × (3.5/2) + (22/7) × (3.5/2) × 3.7] cm^2

= (22/7) × (3.5/2) (3.5+3.7) cm^2

= (11/2) × (3.5 + 3.7) cm^2

= 39.6 cm^2 (approx.)