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A metal container is in the form of a cylinder surmounted by a hemisphere of the same radius. The internal height of the cylinder is $7 m$ and the internal radius of the cylinder is $3.5 m$ . What is the total surface area of the container?

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360.5 m 2

269.5 m 2

256.5 m 2

368.5 m 2

answer is B.

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Detailed Solution

Given that the internal height of the cylinder is

7 m

and the internal radius of the cylinder is

3.5 m

.
We have the following formulae,
Curved surface area of the cylinder =

2 π r h

Curve surface area of hemisphere

= 2 π r 2

Area of circular base of cylinder

= π r 2

We take h as the height of the cylinder with radius r.
We have that the radius of the hemisphere is the same as the cylinder.
r=3.5 m
h=7m
Total surface area of container = C.S.A of cylinder + C.S.A of hemisphere + Area of circular base of cylinder

= 2 π r h + 3 π r 2 = 2 × 227 × 7 × 3.5 + 3 × 227 × 3.5 × 3.5 = 269.5 m 2

Thus, the total surface area is

269.5 m 2

.
Therefore the correct option is 2.

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