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State true or false.
A wooden article was made by scooping out a hemisphere from each end of a solid cylinder (Fig.). If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, then the total surface area of the article is $374 c m 2$ .

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True

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answer is A.

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Detailed Solution

The given statement is ‘A wooden article was made by scooping out a hemisphere from each end of a solid cylinder (Fig.). If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, then the total surface area of the article is

374 c m 2

’.

Now, the total surface area of the article is;
Total surface area of article = Curved surface area of the cylinder + 2

×

Curved surface area of hemisphere
Using the formula for curved surface area of a cylinder =2πrh and curved surface area of hemisphere

= 2 π r 2

, we get
Total surface area of article

= 2 π r h + 2 × 2 π r 2

Substituting the values, we get

⇒ 2 × 227 × 3.5 × 10 + 2 × 2 × 227 × (3.5) 2 ⇒ 2 × 22 × 5 + 4 × 22 × 0.5 × 3.5 ⇒ 220 + 154 ⇒ 374 c m 2

That is, the total surface area of the wooden article is

374 c m 2

.
Therefore, the given statement is true.
Hence option (1) is correct.

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