Write 'True' or 'False' and justify your answer:
An open metallic bucket is in the shape of a frustum of a cone,mounted on a hollow cylindrical base made of the same metallic sheet. The surface area of the metallic sheet used is equal to curved surface area of frustum of a cone + area of circular base + curved surface area of cylinder.
An open metallic bucket is in the shape of a frustum of a cone,mounted on a hollow cylindrical base made of the same metallic sheet. The surface area of the metallic sheet used is equal to curved surface area of frustum of a cone + area of circular base + curved surface area of cylinder.
(A) True.
The total surface area of the metallic sheet used is the sum of the areas of the individual parts that make up the object.
$1$. The bucket is a frustum of a cone $(ABCD)$,so we include its curved surface area.
$2$. The bucket has a circular base at the bottom of the frustum,which is also the top of the cylinder. However,since the bucket is open and mounted on a cylinder,the metallic sheet used includes the curved surface of the frustum,the curved surface of the cylinder,and the circular base at the bottom of the cylinder $(EF)$.
$3$. The area of the metallic sheet = (Curved surface area of frustum of a cone) + (Curved surface area of cylinder) + (Area of the circular base at the bottom).
As shown in the figure,$ABCD$ is a frustum of a cone and $CDEF$ is a hollow cylinder.
The total surface area of the metallic sheet used is the sum of the areas of the individual parts that make up the object.
$1$. The bucket is a frustum of a cone $(ABCD)$,so we include its curved surface area.
$2$. The bucket has a circular base at the bottom of the frustum,which is also the top of the cylinder. However,since the bucket is open and mounted on a cylinder,the metallic sheet used includes the curved surface of the frustum,the curved surface of the cylinder,and the circular base at the bottom of the cylinder $(EF)$.
$3$. The area of the metallic sheet = (Curved surface area of frustum of a cone) + (Curved surface area of cylinder) + (Area of the circular base at the bottom).
As shown in the figure,$ABCD$ is a frustum of a cone and $CDEF$ is a hollow cylinder.
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