RD Sharma Class 9 Solutions Chapter 20 Surface Areas and Volume of A Right Circular Cone MCQs

In this chapter, we provide RD Sharma Solutions for Chapter 20 Surface Areas and Volume of A Right Circular Cone MCQS for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Solutions for Chapter 20 Surface Areas and Volume of A Right Circular Cone MCQS Maths pdf, free RD Sharma Solutions for Chapter 20 Surface Areas and Volume of A Right Circular Cone MCQS Maths book pdf download. Now you will get step by step solution to each question.

TextbookNCERT
ClassClass 9
SubjectMaths
ChapterChapter 20
Chapter NameSurface Areas and Volume
of A Right Circular Cone
ExerciseMCQS

RD Sharma Solutions for Class 9 Chapter 20 Surface Areas and Volume of A Right Circular Cone MCQS Download PDF

Question 1.
The number of surfaces of a cone has, is
(a) 1
(b) 2
(c) 3
(d) 4
Solution:
Number of surfaces of a cone are 2 (b)

Question 2.
The area of the curved surface of a cone of radius 2r and slant height 12, is
RD Sharma Class 9 Chapter 20 Surface Areas and Volume of A Right Circular Cone
Solution:
Radius of a cone = 2r
RD Sharma Class 9 Solutions Chapter 20 Surface Areas and Volume of A Right Circular Cone

Question 3.
The total surface area of a cone of radius r2 and length 2l, is
RD Sharma Solutions Class 9 Chapter 20 Surface Areas and Volume of A Right Circular Cone
Solution:
RD Sharma Class 9 PDF Chapter 20 Surface Areas and Volume of A Right Circular Cone

Question 4.
A solid cylinder is melted and cast into a cone of same radius. The heights of the cone and cylinder are in the ratio
(a) 9 : 1
(b) 1 : 9
(c) 3 : 1
(d) 1 : 3
Solution:
Let r be the radius and h be the height of cylinder, then volume = πr2h
Now volume of cone = πr2h
r is the radius
Surface Areas and Volume of A Right Circular Cone Class 9 RD Sharma Solutions
RD Sharma Class 9 Solution Chapter 20 Surface Areas and Volume of A Right Circular Cone

Question 5.
If the radius of the base of a right circular cone is 3r and its height is equal to the radius of the base, then its volume is
Class 9 RD Sharma Solutions Chapter 20 Surface Areas and Volume of A Right Circular Cone
Solution:
Radius of the base of a cone (R) = 3r
and height (H) = 3r
Class 9 Maths Chapter 20 Surface Areas and Volume of A Right Circular Cone RD Sharma Solutions

Question 6.
If the volumes of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5, then the ratio of their heights, is
(a) 1 : 5
(b) 5 : 4
(c) 5 : 16
(d) 25 : 64
Solution:
Ratio in the volumes of two cones =1:4
and ratio in their diameter = 4:5
Let h1, h2 be their heights
RD Sharma Book Class 9 PDF Free Download Chapter 20 Surface Areas and Volume of A Right Circular Cone
RD Sharma Class 9 Book Chapter 20 Surface Areas and Volume of A Right Circular Cone

Question 7.
The curved surface area of one cone is twice that of the other while the slant height of the latter is twice that of the former. The ratio of their radii is
(a) 2 : 1
(b) 4 : 1
(c) 8 : 1
(d) 1 : 1
Solution:
Let r be the radius and l be the slant height
∴ Curved surface area of first cone = πr1l1
and let curved surface area of second cone = πr2l2
Surface Areas and Volume of A Right Circular Cone With Solutions PDF RD Sharma Class 9 Solutions

Question 8.
If the height and radius of a cone of volume V are doubled, then the volume of the cone, is
(a) 3V
(b) 4V
(c) 6V
(d) 8V
Solution:
Let r and h be the radius and height of a cone, then
RD Sharma Class 9 Maths Book Questions Chapter 20 Surface Areas and Volume of A Right Circular Cone

Question 9.
The ratio of the volume of a right circular cylinder and a right circular cone of the same base and height, is
(a) 1 : 3
(b) 3 : 1
(c) 4 : 3
(d) 3 : 4
Solution:
Let r be the radius and h be the height of a right circular cylinder and a right circular cone, and V1 and V2 are their volumes, the V1 =  πr2h and
RD Sharma Mathematics Class 9 Solutions Chapter 20 Surface Areas and Volume of A Right Circular Cone

Question 10.
A right cylinder and a right circular cone have the same radius and same volumes. The ratio of the height of the cylinder to that of the cone is
(a) 3 : 5
(b) 2 : 5
(c) 3 : 1
(d) 1 : 3
Solution:
Let r be the radius of cylinder and cone and volumes are equal
and h1, and h2 be their have h2 is respectively
RD Sharma Math Solution Class 9 Chapter 20 Surface Areas and Volume of A Right Circular Cone

Question 11.
The diameters of two cones are equal. If their slant heights are in the ratio 5 : 4, the ratio of their curved surface areas, is
(a) 4 : 5
(b) 25 : 16
(c) 16 : 25
(d) 5 : 4
Solution:
∵ Diameters of two cones are equal
∴ Their radii are also be equal
Let r be their radius of each cone,
and ratio in their slant heights = 5:4
Let slant height of first cone (h1) = 5x
Then height of second cone (h2) = 4x
RD Sharma Class 9 Questions Chapter 20 Surface Areas and Volume of A Right Circular Cone

Question 12.
If the heights of two cones are in the ratio of 1 : 4 and the radii of their bases are in the ratio 4 : 1, then the ratio of their volumes is
(a) 1 : 2
(b) 2 : 3
(c) 3 : 4
(d) 4 : 1
Solution:
Ratio in the heights of two cones =1 : 4
and ratio in their radii of their bases = 4 : 1
Let height of the first cone = x
and height of the second cone = 4x
Radius of the first cone = 4y
and radius of the second cone = y
Maths RD Sharma Class 9 Chapter 20 Surface Areas and Volume of A Right Circular Cone

Question 13.
The slant height of a cone is increased by 10%. If the radius remains the same, the curved surface area is increased by
(a) 10%
(b) 12.1%
(c) 20%
(d) 21%
Solution:
Let r be radius and l be the slant height of a cone, then curved surface area = πrl
If slant height is increased by 10%, then
Maths RD Sharma Class 9 Chapter 20 Surface Areas and Volume of A Right Circular Cone
RD Sharma Class 9 Solutions Chapter 20 Surface Areas and Volume of A Right Circular Cone MCQS 13a

Question 14.
The height of a solid cone is 12 cm and the area of the circular base is 6471 cm2. A plane parallel to the base of the cone cuts through the cone 9 cm above the vertex of the cone, the area of the base of the new cone so formed is
(a) 9π cm2
(b) 16π cm2
(c) 25π cm2
(d) 36π cm2
Solution:
Height of a solid cone (h) = 12 cm
Area of circular base = 64π cm2
RD Sharma Class 9 PDF Chapter 20 Surface Areas and Volume of A Right Circular Cone
Surface Areas and Volume of A Right Circular Cone Class 9 RD Sharma Solutions

Question 15.
If the base radius and the height of a right circular cone are increased by 20%, then the percentage increase in volume is approximately
(a) 60
(b) 68
(c) 73
(d) 78
Solution:
In first case,
Let r be radius and h be height, in volume
Class 9 RD Sharma Solutions Chapter 20 Surface Areas and Volume of A Right Circular Cone

Question 16.
If h, S and V denote respectively the height, curved surface area and volume of a right circular cone, then 3πVh3 – S2h2 + 9V2 is equal to
(a) 8
(b) 0
(c) 4π
(d) 32π2
Solution:
h = height, S = curved surface area
V = volume of a cone
Let r be the radius of the cone, then
Class 9 Maths Chapter 20 Surface Areas and Volume of A Right Circular Cone RD Sharma Solutions

Question 17.
If a cone is cut into two parts by a horizontal plane passing through the mid¬point of its axis, the ratio of the volumes of upper and lower part is
(a) 1 : 2
(b) 2 : 1
(c) 1 : 7
(d) 1 : 8
Solution:
∴ ∆PDC ~ ∆PBA (AA axiom)
and O’ is mid point of PO
RD Sharma Book Class 9 PDF Free Download Chapter 20 Surface Areas and Volume of A Right Circular Cone
RD Sharma Class 9 Book Chapter 20 Surface Areas and Volume of A Right Circular Cone
Surface Areas and Volume of A Right Circular Cone With Solutions PDF RD Sharma Class 9 Solutions

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