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Question 3
Write ‘True’ or ‘False’ and justify your answer in the following.

A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid is πrr2+h2+3r+2h

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Solution

The given statement is false.

We know that,
The total surface area of a cone of radius r
and height h
= curved surface Area + area of base
=πrl+πr2

Where, l=h2+r2

The total surface area of a cylinder of base radius r and hegith h
= Curved surface area + Area of both base
=2πrh+2πr2

Here, when we placed a cone over a cylinder, then one base is common for both.

So, total surface area of the combined solid
=πrl+2πrh+πr2
=π[l+2h+r]=πr[r2+h2+2h+r] (l=r2+h2)

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