Write ‘True’ or ‘False’ and justify your answer in the following:
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 the curved surface area of the frustum of a cone + area of circular base + the curved surface area of cylinder
Answer True
Solution
According to the question, here is a metallic bucket 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 Figure (A) is the surface area of (a), (b), (c)
(a) = curved surface area of frustum
(b) = area of circular base
(c) = curved area of cylinder
Total surface area = curved surface area of a frustum of cone + area of circular base + curved surface area of the cylinder.
So the given statement is True.
View Full Answer(1)Write ‘True’ or ‘False’ and justify your answer in the following:
The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the Figure is
AnswerTrue
Solution
It is given that a cylindrical vessel of height h and radius r is raised upward with a hemispherical portion.
From the figure radius of the hemisphere = r cm
The volume of the figure = volume of the cylinder – the volume of the hemisphere
So the given statement is True.
View Full Answer(1)Write ‘True’ or ‘False’ and justify your answer in the following :
A solid ball is exactly fitted inside the cubical box of side a. The volume of the ball is
It is given that the ball is exactly filled inside the cubical box of side a.
Hence the diameter of the sphere = a
Hence the given statement is False.
View Full Answer(1)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 the same base radius and height as that of a cone. The total surface area of the combined solid is
It is given that there is a cone of radius r and height h and a cylinder of height h and radius r.
Where A is placed on B
Total surface area = Surface area of cone + Total surface area of cylinder – Surface area of part I – the surface area of part II
The total surface area is not equal to
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Write ‘True’ or ‘False’ and justify your answer in the following :
A solid cylinder of radius r and height h is placed over other cylinders of the same height and radius. The total surface area of the shape so formed is
It is given that there are two cylinders of height h and radius r.
Where one is placed on another then the shape formed is
The total surface area of the shape formed
So the surface area is not equal to
Write ‘True’ or ‘False’ and justify your answer in the following:
Two identical solid hemispheres of equal base radius r cm are stuck together along their bases. The total surface area of the combination is .
It is given that there are two hemispheres of radius r.
Let A and B be two hemispheres of radius r.
Join A and B along with their bases
Now it is a full sphere of radius r
The total surface area of a sphere
Here we found that the total surface area of the combination is , but not
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Write True or False and justify your answer:
In a triangle, the sides are given as 11 cm, 12 cm and 13 cm. The length of the altitude is 10.25 cm corresponding to the side having length 12 cm.
True
Hence the area obtained is the same.
Therefore the given statement is true.
View Full Answer(1)Write True or False and justify your answer:
The cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of Rs is Rs 918.
Solution
We know that using Heron’s formula
=
To find cost :
Cost of levelling 1 m2 = Rs 3
Therefore the given statement is true.
View Full Answer(1)Write True or False and justify your answer:
The area of a regular hexagon of side ‘a’ is the sum of the areas of the five equilateral triangles with side a.
Solution
According to question
We know that a regular hexagon is divided into 6 equilateral triangles by its diagonals.
Therefore the given statement is false.
View Full Answer(1)Write True or False and justify your answer:
The base and the corresponding altitude of a parallelogram are 10 cm and 3.5 cm, respectively. The area of the parallelogram is 30
[False]
We know that
Hence, area of parallelogram is
Therefore the given statement is false.
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