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A vessel is in the form of a hemispherical bowl, surmounted by a hollow cylinder. The diameter of the hemisphere is $12 cm$ and the total height of the vessel is $16 cm$ . Find the surface area of the vessel. (Take $π$ = $3.14$ ).

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602.88 {cm}^{2}

606.81 {cm}^{2}

666.89 {cm}^{2}

467.78 {cm}^{2}

answer is A.

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Detailed Solution

Given,
The height of the vessel is

16 cm

.
The diameter of the hemispherical bowl is

12 cm

.
The radius of the hemisphere (r) is

\frac{12}{2} = 6 cm

.
The height of the cylindrical part (h)=

(16 - 6) cm

\Rightarrow

10 cm

The curved surface area of the bowl=

2 π r^{2}

\Rightarrow

2 \times 3.14 \times 6 \times 6 cm

\Rightarrow

226.08 {cm}^{2}

The surface area of the cylinder =

2 πr h

\Rightarrow

2 \times 3.14 \times 6 \times 10 {cm}^{2}

\Rightarrow 376.8 {cm}^{2}

The surface area of the vessel = Surface area of the cylinder + Surface area of the sphere

\Rightarrow

(377.14 + 226.28) {cm}^{2}

\Rightarrow

602.88 {cm}^{2}

Therefore, surface area of the vessel is

602.88 {cm}^{2}

.
Hence, the correct option is 1.

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