SESSION : 6
Geometry and Mensuration 3D
Cube, Sphere, Hemisphere, Cylinder, Cone
GUIDA
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References
1 2 3
NCERT Class 8 NCERT Class 9 NCERT Class 10
Mathematics: Mathematics: Mathematics:
Chapter 11 Chapter 13 Surface Chapter 13 Surface
Mensuration Areas and Volumes Areas and Volumes
2
Why some questions are difficult to solve ?
HARD CONCEPT THE PHRASING OF THE QUESTION CONTAINS LENGTHY NUMERICAL
LEADS TO CONFUSIONS CALCULATIONS
3
Concept of Volume
4
Previous Year Question 2023
1) The volume of a wall which is 5 times as high as it is broad and 8
times as long as it is high, is 12.8 𝑚3 . The breadth of the wall is
1. 40 cm
2. 50 cm
3. 60 cm
4. 70 cm
5
Cube
6
Previous Year Question 2023
2) The volumes of 3 solid cubes made of metal are 125 𝑐𝑚3 , 64 𝑐𝑚3
and 27 𝑐𝑚3 respectively. After melting all the three cubes a solid cube
is made. Find the edge of the new cube.
(1) 2.5 cm
(2) 4 cm
(3) 6 cm
(4) 5 cm
7
Sphere & Hemisphere
8
Previous Year Questions
3) A capsule of medicine is in the shape of a sphere of diameter 2.8 mm. How much
medicine is needed to fill this capsule (correct to one decimal place)?
1. 11.5 𝑚𝑚3
2. 1 𝑚𝑚3
3. 22.4 𝑚𝑚3
4. 15.4 𝑚𝑚3
9
Cylinder
10
Previous Year Question 2023
4) The base radius of a cylinder is 5 m more than its height. If the curved surface
area of the cylinder is 792 𝑚2 , then what is the volume of the cylinder (in 𝑚3 )?
Use 𝜋 = 22/7
(1) 5306
(2) 5244
(3) 5544
(4) 5462
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DOMAIN I TITLE 12
Previous Year Question 2023
5) If the base radius of a cylinder is doubled, then how many times will
its volume become with respect to its original volume?
1.2
2.4
3.6
4.8
13
Previous Year Question 2023
6) If a rectangular sheet of paper of length 6 cm and width 3 cm is rolled to form a
cylinder with height equal to the width of the paper, then what is the base radius of
the cylinder (in cm) ?
(1) 6/ π
(2) 3/ π
(3) 3/2 π
(4) 9/2 π
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Cone
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Previous Year Question 2023
7) A toy is made in the shape of a hemisphere of diameter 7 cm surmounted by a
cone. If total height of the toy is 15.5 cm, and toy is polished at 20 paise per 𝑐𝑚2 ,
then find the cost of polishing. Take π = 22/7
(1) 39 Rupees
(2) 40.50 Rupees
(3) 42.90 Rupees
(4) 45 Rupees
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DOMAIN I TITLE 17
DOMAIN I TITLE 18
Previous Year Question 2023
8) The ratio of the base radii of a cylinder and a cone is 3:4 and their
heights are in the ratio 2:3. Then the ratio of their volume:
1. 8:9
2.9:8
3. 7:13
4. 12:15
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DOMAIN I TITLE 20
Coordinate Geometry
Quadrants, Slope, Distance formula, Centroid
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Cartesian Coordinates and Quadrants
22
Previous Year Question 2023
9) The point (-2, 3) lies in which quadrant?
1. I
2. II
3. III
4. IV
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Previous Year Question 2023
10) In which quadrants do the points (-2, 3) and (3,-2) lie?
1. Both in second quadrant
2. First and Fourth quadrants
3. Second and Third quadrants
4. Second and Fourth quadrants
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Slope
25
Previous Year Question 2023
11) A quadrilateral has vertices in the order (0, -1), (-2, 3), (6, 7) and (8, 3). The
quadrilateral is a :
(1) Trapezium
(2) Square
(3) Rhombus
(4) Rectangle
26
Previous Year Question 2023
12) If the points A(6, 1), B(8, 2), C(9, 4) and D(7, k) are the vertices of a
parallelogram taken in order, then find the value of k.
(1) 3
(2) 5
(3) 7
(4) 9
27
Distance Formula
28
Previous Year Question 2023
13) Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9).
(1) (-7,0)
(2) (7,0)
(3) (-5, 0)
(4) (5,0)
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Centroid
30
Previous Year Question 2023
14) If the vertices of a triangle ABC are A(1,3), B(3,5) and C(x, y) and centroid is
(11/3, 16/3) then (x, y) is:
1. (8, 7)
2. (7, 8)
3. (4, 8)
4. (7,7)
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THANKS…
GUIDA
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