9th Standard CBSE Syllabus & Materials
9th Standard CBSE
CBSE 9th Standard Mathematics Statistics Sample Question Papers Study Material - QB365 Set D
NEW9th Standard CBSE
CBSE 9th Standard Mathematics Statistics Sample Question Papers Study Material - QB365 Set C
NEW9th Standard CBSE
CBSE 9th Standard Mathematics Statistics Sample Question Papers Study Material - QB365 Set B
NEW9th Standard CBSE
CBSE 9th Standard Mathematics Statistics Sample Question Papers Study Material - QB365 Set A
NEW9th Standard CBSE
CBSE 9th Standard Mathematics Surface Areas and Volumes Sample Question Papers Study Material - QB365 Set D
NEW9th Standard CBSE
CBSE 9th Standard Mathematics Surface Areas and Volumes Sample Question Papers Study Material - QB365 Set B
Published on: 29/10/2025
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Questions + Answers key
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1.
The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the radius of the base of cylinder.
2.
Simplify: \(\left( x+\frac { 1 }{ x } \right) \left( x-\frac { 1 }{ x } \right) \left( { x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } \right) \left( { x }^{ 4 }+\frac { 1 }{ { x }^{ 4 } } \right) \)
3.
In the given figure, if AB = CD, then prove that AC = BD. Also write the Euclid's axiom used for proving it.
4.
Find the value of k, if x-2 is a factor of p(x) = x2+kx+2k.
5.
What is the volume of a cube whose total surface area is 864 m2?
6.
Find the curved surface area of a right circular cone, whose slant height is 10 cm and base radius is 7 cm.
7.
The perimeter of a triangular ground is 900 m and its sides are in the ratio 3: 5 : 4. Using Heron's formula, find the area of the ground.
8.
In figure, O is the centre of the circle. If \(\angle AOB= 80°\). then find the measures of \(\angle ABD\) and \(\angle ACB\) .
9.
In the figure, O is the centre of the circle. Arc BCD subtends an angle of 140° at the centre. BC is produced to P and CD is joined. Find measure of \(\angle DCP\).
10.
Two concentric circles are with centre O. A, B, C, D are the points of intersection with a line. If AD = 12 cm and BC = 8 cm, find the length of AB, CD, AC and BD.
11.
In the given figure find the value of x and y if AB || CD
12.
In the figure AB || CD and CD || EF Also \(EA\bot AB\) if \(\angle BEF=55^{ 0 }\) find the values of x,y and z
13.
Factorise: \(2\sqrt{2}a^3+16\sqrt{2}b^3+c^3-12abc\)
14.
If \(x^2+\frac{1}{x^2}=7\) find the value of \(x^3+\frac{1}{x^3}\)
15.
Factorise: \(x^3-3x^2-9x-5\)
16.
If \(p(x)=x^3-ax^2+bx+3 \)leaves a remainder-19 when divided by (x+2) and a remainder 17 when divided by (x-2), prove that a+b=6
17.
Using long division method divide the polynomial \(3x^4-4x^3-3x-1\) by \(1-x\)
18.
If \(a+8\sqrt { 5 } b=\frac { 8+\sqrt { 5 } }{ 8-\sqrt { 5 } } +\frac { 8-\sqrt { 5 } }{ 8+\sqrt { 5 } } \) , find a and b.
19.
Simplify \(5\sqrt { 8 } +2\sqrt { 32 } -2\sqrt { 2 } \)
1.
Given, CSA of a cylinder = 88 cm2
height = 14 cm
CSA of a cylinder = 2\(\pi\)rh
\(\Rightarrow \ 88=2\times \frac { 22 }{ 7 } \times r\times 14\)
\(\Rightarrow \ r=\frac { 88\times 7 }{ 2\times 22\times 14 } \)
= 1 cm
2.
\(\left( x+\frac { 1 }{ x } \right) \left( x-\frac { 1 }{ x } \right) \left( { x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } \right) \left( { x }^{ 4 }+\frac { 1 }{ { x }^{ 4 } } \right) \)
\(=\left( { x }^{ 2 }-\frac { 1 }{ { x }^{ 2 } } \right) \left( { x }^{ 2 }+\frac { 1 }{ { x }^{ 2 } } \right) \left( { x }^{ 4 }+\frac { 1 }{ { x }^{ 4 } } \right) \)
as (a+b)(a-b)=a2-b2
\(=\left( { x }^{ 4 }-\frac { 1 }{ { x }^{ 4 } } \right) \left( { x }^{ 4 }+\frac { 1 }{ { x }^{ 4 } } \right) \)
\(=\left( { x }^{ 8 }-\frac { 1 }{ { x }^{ 8 } } \right) \)
3.
AB = CD(Given)
\(\Rightarrow\)AB + BC = BC + CD
\(\Rightarrow\)AC = BD
Euclid's axiom used: If equals are added to equals, the wholes are equal.
4.
(x-2) is a factor of f(x) = x2+kx+2k
f(2) = 0
\(\Rightarrow\) (2)2+k(2)+2k = 0
\(\Rightarrow\) 4 + 2k + 2 = 0
\(\Rightarrow\) 4+4k = 0
\(\Rightarrow\) k = -1
5.
1728 m3
6.
Curved surface area = \(\pi\)rl
\(=\frac{22}{7} \times 7 \times 10 \mathrm{~cm}^{2}\)
= 220 cm2
7.
33750 cm2
8.
40°, 40°
9.
70°
10.
2, 2, 10, 10 (in cm)
11.
\(x=42^{ 0 },y=38^{ 0 }\)
12.
Given AB||CD, CD||EF, \(EA\bot AB\)
\(\angle BEF=55^o\)
y = 180o- 55o = 125o(Co-interior angles)
x = y = 125o(Corresponding angles)
\(EA\bot AB\)
\(EA\bot AB\)
Z + 55o = 90o
Z = 90o - 55o
= 35o
13.
\((\sqrt{2}a+2\sqrt{2}b+c)(2a^2+8b^2+c^2-4ab-4\sqrt{2}bc-2\sqrt{2ac})\)
14.
18
15.
(x+1)(x+1)(x-5)
16.
a=1, b=5
17.
Quotient =\(3x^3-x^3-x-1\)
Remainder=-5
18.
\(a=\frac { 138 }{ 59 } ,b=0\)
19.
0
9th Standard CBSE Syllabus & Materials
9th Standard CBSE
CBSE 9th Standard Mathematics Surface Areas and Volumes Sample Question Papers Study Material - QB365 Set A
NEW9th Standard CBSE
CBSE 9th Standard Mathematics Heron's Formula Sample Question Papers Study Material - QB365 Set D
NEW9th Standard CBSE
CBSE 9th Standard Mathematics Heron's Formula Sample Question Papers Study Material - QB365 Set C
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