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A wooden article as shown in the figure was made from a cylinder by scooping out a hemisphere from one end and a cone from the other end. What is the total surface area of the article?

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315.8 c m 2

310 c m 2

312.2 c m 2

211.2 c m 2

answer is A.

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Detailed Solution

Given that the height of the cylinder is 10cm, height of the cone is 7cm and the diameter of the base of the cylinder is 6cm.
Question Image

We have the following formula,
The curved surface area of a cone

= π r h

The curved surface area of a cylinder

= 2 π r h

The curved surface area of a hemisphere

= 2 π r 2

The total surface area will be,
Diameter is 6cm then, the radius will be 3cm.
Slant height for cone=

l = h 2 + r 2 l = 72 + 32 l = 49 + 9 l = 7.61 c m

Total surface area= the curved surface area of (Cone + cylinder +hemisphere)

= 3.14 × 3 (7.61 + 2 × 10 + 2 × 3) = 9.4 (33.61) = 315.8 c m 2

Thus the total surface area of the article is

315.8 c m 2

.
Therefore the correct option is 1.

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