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A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the total surface area of the vessel. (Use $π = \frac{22}{7}$ )

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1354 {cm}^{2}

1144 {cm}^{2}

1254 {cm}^{2}

1354 {cm}^{2}

answer is B.

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Detailed Solution

Given,
Hemispherical bowl's diameter = 14 cm.
So, Hemispherical bowl’s radius

r = \frac{14}{2} = 7 cm

.
Now, Height of the entire vessel

= 13 cm

Here,
The cylinder's height (h) = Height of the entire vessel - Hemispherical bowl’s radius

h = 13 cm - 7 cm

h = 6 cm

We now,
Surface area overall = 2 (Cylindrical surface area + hemispherical surface area)

= 2 (2 πrh + 2 π r^{2})

= 4 πr (h + r)

= 4 \times \frac{22}{7} \times 7 \times (6 + 7) {cm}^{2}

= 1144 {cm}^{2}

Thus, the total surface area of the vessel

= 1144 {cm}^{2}

Correct option is 2.

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