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If a solid cone of base radius r and height h is placed over a solid cylinder having same base radius and height as that of the cone, then the curved surface area of the shape is πr√(h² + r²) + 2πrh. Write ‘True’ or ‘False’ and justify your answer

Solution:

It is given that

Base radius of a solid cone = r

Height of a solid cone = h

Base radius of a solid cylinder = r

Height of the solid cylinder = h

If a solid cone of base radius r and height h is placed over a solid cylinder having same base radius and height as that of the cone, then the curved surface area of the shape is

So the curved surface area of the shape = Curved surface area of cone + Curved surface area of cylinder

= πrl + 2πrh

It can be written as

= \(\pi r\sqrt{h^{2}+r^{2}}+2\pi rh\)

Therefore, the statement is true.

✦ Try This: A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is equal to the radius of the cone.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13

NCERT Exemplar Class 10 Maths Exercise 12.2 Sample Problem 1

If a solid cone of base radius r and height h is placed over a solid cylinder having same base radius and height as that of the cone, then the curved surface area of the shape is πr√(h² + r²) + 2πrh. Write ‘True’ or ‘False’ and justify your answer

Summary:

The statement “If a solid cone of base radius r and height h is placed over a solid cylinder having same base radius and height as that of the cone, then the curved surface area of the shape is πr√(h² + r²) + 2πrh” is true

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