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.
Explore More
Similar Questions
The base of a cone with radius $5 \, cm$ and height $12 \, cm$ is hemispherical. Find the total surface area of the article. $(\pi = 3.14)$ (in $cm^2$)
Medium
View SolutionTotal surface area of a cylinder with radius $7 \, cm$ and height $13 \, cm$ is $\ldots \ldots \ldots \ldots \, cm^{2}$.
Easy
View SolutionTotal surface area of a hemisphere with diameter $2 \, cm$ is $\ldots \ldots \ldots cm^{2}$.
Easy
View Solution$A$ cubical block of side $7 \, cm$ is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid (in $cm^2$). [Use $\pi = \frac{22}{7}$]
Medium
View Solution$A$ fez,the cap used by the Turks,is shaped like the frustum of a cone (see $Fig.$). If its radius on the open side is $10 \, cm$,radius at the upper base is $4 \, cm$ and its slant height is $15 \, cm$,find the area of material used for making it.
Medium
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo