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Q.

State true or false.

A solid cone of radius r and height h is placed over a solid cylinder having the same base radius and height as that of a cone. The total surface area of the combined solid is $π r 2 + h 2 + 3 r + 2 h$ .

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a

True

b

False

answer is B.

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Detailed Solution

Given that a solid cone of radius r and height h is placed over a solid cylinder having the same base radius and height as that of a cone.
The total surface area of the solid cone is

π r l + π r 2

, and the total surface area of the solid cylinder is

2 π r r + h

.
The total surface area of the combined solid is the sum of the surface area of the cone, curved surface area of the cylinder and area of the base of the cylinder. The slant height can be written as,

l = r 2 + h 2

. So,

A = π r l + 2 π r h + π r 2 A = π r l + 2 h + r A = π r r 2 + h 2 + 2 h + r

The given statement is false, and the total surface area of the combined solid is

A = π r r 2 + h 2 + 2 h + r

.
Therefore, 2 is the correct option.

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