Mathematics

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder (as shown in the adjoining figure). If the height of the cylinder is 10 cm and its base is of radius 3.5 cm, find the total surface area of the article.

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Height of the cylinder = 10 cm

Radius of the cylinder= 3.5 cm

Total surface area (T) = Curved surface area of cylinder + 2 × curved surface area of hemisphere

T = 2πrh + 2 × 2πr²
T = 2πr(h + 2r)

Putting values we get,

$\text{T} = 2 \times \dfrac{22}{7} \times 3.5 \times (10 + 7) \\[1em] = \dfrac{154}{7} \times 17 \\[1em] = 22 \times 17 \\[1em] = 374 \text{ cm}^2.$

Hence, the total surface area of the article is 374 cm².

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