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A cup is in the form of a hemisphere surmounted by a cylinder. The height of the

cylindrical portion is 8cm and the total height of the cup is 11.5cm. Find the total

surface area of the cup. $(Take π = \frac{22}{7})$

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253 sq . cm .

255 sq . cm .

258 sq . cm .

252 sq . cm .

answer is A.

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Detailed Solution

Given,
The height of the cylindrical portion =8 cm the total height of the cup= 11.5 cm.
So, hemispherical portion:
Radius

r =

Total height =8

\Rightarrow r = 11.5 - 8

\Rightarrow r = 3.5 cm

thus, radius,

r = 3.5 cm

r = \frac{7}{2} cm

Now, cup’s Total surface area can be given as,
= curved surface area of the hemispherical portion+ curved surface area of the cylindrical portion

= 2 π r^{2} + 2 πrh = 2 πr (r + h)

= 2 \times \frac{22}{7} \times \frac{7}{2} (\frac{7}{2} + 8)

= 253 sq . cm

Hence, total surface area of cup = 253sq.cm.
The Correct Answer is 1.

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