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

Chapter/Topic: Surface area and volumes

Question

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

Chapter/Topic: Surface area and volumes

Accepted Answer

Here, we have been given that a cup is in the form of a hemisphere surmounted by a cylinder. Let us draw a rough diagram of the given situation.
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In the above diagram, we are assuming the height of the cylinder as ‘h’ and radius of cylinder = radius of hemisphere = r.
Now, it is given that the height of the cylindrical portion is 8cm and the total height of the cup is 11.5cm. So, we have,
Hemispherical portion:
Radius r= Total height −8
⇒ r=11.5−8=3.5cm
Cylindrical portion
Height, h=8cm
thus, radius r=3.5cm=

\frac{7}{2}

cm
Therefore, the radius of the cylinder and the hemisphere are 3.5cm each.
Since, the given thing is a cup so it will be hollow from inside in which some liquid can be filled. So, the total surface area of the cup will be the sum of the curved surface area of the cylinder and the curved surface area of the hemisphere. We know that, curved surface area of cylinder = 2πrh and curved surface area of hemisphere = 2πr2 , therefore, we have,
⇒ Total surface area of the cup= Curved Surface Area of the hemispherical portion+ Curved Surface Area of the cylindrical portion
2πr2+2πrh=2πr(r+h)
=2×