Question

If a lemon of radius r is divided into four identical parts, then what would be the total surface area of the four parts? (Given area of a sphere =4π r²) ​

Answer 1

Answer:

The total surface area of the four parts will be 8πr² units².

Step-by-step explanation:

Given :

➻ Radius of lemon = r units

➻ Radius of each part = r units

➻ Divided into = 4 identical parts

Now, each part has :

➻ Curved surface = 1

➻ Semicircular faces = 2

Let's now calculate the area for one part :

➻ Ar. = ¼ CSA of sphere + 2 Ar. of semicircle

➻ Ar. = ¼ × 4πr² + 2 × ½ × πr²

➻ Ar. = πr² + πr²

➻ Ar. of one part = 2πr² units²

Finally, area of 4 parts :

➻ Ar. of 4 parts = Ar. of one part × 4

➻ Ar. of 4 parts = 2πr² units² × 4

➻ Ar. of 4 parts = 8πr² units²

Therefore, the TSA of the four parts is 8πr² units².

Formulae used:

The formulae used in the above solution are :

➻ Ar. of semicircle = ½ πr²

➻ CSA of sphere = 4πr²

Answer 2

Answer:

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Step-by-step explanation:

Radius of lemon = r units

➻ Radius of each part = r units

➻ Divided into = 4 identical parts

Now, each part has :

➻ Curved surface = 1

➻ Semicircular faces = 2

Let's now calculate the area for one part :

➻ Ar. = ¼ CSA of sphere + 2 Ar. of semicircle

➻ Ar. = ¼ × 4πr² + 2 × ½ × πr²

➻ Ar. = πr² + πr²

➻ Ar. of one part = 2πr² units²

Finally, area of 4 parts :

➻ Ar. of 4 parts = Ar. of one part × 4

➻ Ar. of 4 parts = 2πr² units² × 4

➻ Ar. of 4 parts = 8πr² units²

Therefore, the TSA of the four parts is 8πr² units².