Mathematics
The given figure shows a toy made of very thin metal sheet. The toy has the hemisphere, a cylinder and a cone all of the same radius.
Assertion(A): The minimum area of metal sheet required is:
Curved surface area of conical part + curved surface area of cylinder part - curved surface area of hemispherical part
Reason(R): Metal sheet required = curved surface area of (conical part + cylindrical part + hemispherical part)
A is true, R is false.
A is false, R is true.
Both A and R are true and R is correct reason for A.
Both A and R are true and R is incorrect reason for A.
Answer
The toy has the hemisphere, a cylinder and a cone all of the same radius.
Metal sheet required = minimum area of metal sheet required
= curved surface area of conical part + curved surface area of cylinder part + curved surface area of hemisphere part
= curved surface area of (conical part + cylindrical part + hemispherical part)
∴ A is false, R is true.
Hence, option 2 is the correct option.
Related Questions
A solid metal cuboid with dimension 10 cm, 11 cm and 8 cm is melted and identical solid spheres, each of radius 1 cm, are formed. The number of sphere formed is :
105
210
315
420
By applying force on an uniform metallic wire, the wire is extended four times along its length with same width all around. Then :
(i) The volume of metal in both the cases is same.
(ii) The surface area of solid wires in both the cases is same.
Which of the above statements is/are true?
only (i)
only (ii)
both (i) and (ii)
neither (i) nor (ii)