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Surface Class 9

The document contains a series of mathematical problems related to surface area and volume, including calculations for cones, cylinders, spheres, and cuboids. It also explores concepts such as ratios of dimensions, maximum capacity, and transformations between different shapes. Each problem requires applying geometric formulas to find specific measurements or relationships.

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Raksha Gupta
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27 views1 page

Surface Class 9

The document contains a series of mathematical problems related to surface area and volume, including calculations for cones, cylinders, spheres, and cuboids. It also explores concepts such as ratios of dimensions, maximum capacity, and transformations between different shapes. Each problem requires applying geometric formulas to find specific measurements or relationships.

Uploaded by

Raksha Gupta
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Surface, Area & Volume

1. How much ice-cream can be put into a cone with base radius 3.5 cm and height
12 cm
2. If a wooden box of dimensions 8 m x 7 m x 6 m is to carry boxes of dimensions
8 cm x 7 cm x 6 cm, then find the maximum number of boxes that can be
carried in the wooden box.
3. Two cubes of edge 6 cm are joined to form a cuboid. Find the total surface area
of the cuboid.
4. If in a cylinder, radius is doubled and height is halved, then find its curved
surface area.
5. The radii of two cylinders of the same height are in the ratio 4 :5, then find the
ratio of their volumes.
6. Find the area of the sheet required to make closed cylindrical vessel of height
1 m and diameter 140 cm.
7. Find the volume of cone of radius r/2 and height ‘2h’.
8. A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and
recast into a sphere. Find the radius of the sphere.
9. If the volume of a sphere is numerically equal to its surface area, then find the
diameter of the sphere.
10. The radius of a spherical balloon increases from 6 cm to 12 cm as air is being
pumped into it. Then what will be the ratio of surface areas of the original
balloon to the resulting new balloon ?
11. The outer and the inner radii of a hollow sphere are 12 cm and 10 cm. Find its
volume.
12. In a cylinder, if radius is halved and height is doubled, then find the volume
with respect to original volume.
13. A spherical ball is divided into two equal halves. If the curved surface area of
each half is 56.57 cm?, find the volume of the spherical ball. [use π = 3.14]
14. Find the length of the longest pole that can be put in a room of dimensions 10
m x 10 m x 5 m.
15. Find the capacity in litres of a conical vessel having height 8 cm and slant
height 10 cm.
16. Calculate the surface area of a hemispherical dome of a temple with radius 14
m to be whitewashed from outside.
17. A school provides milk to the students daily in cylindrical glasses of diameter
7 cm. If the glass is filled with milk up to a height of 12 cm, find how many litres
of milk is needed to serve 1600 students.
18. A dome of a building is in the form of a hemisphere. From inside, it was
whitewashed at the cost of Rs 498.96. If the rate of whitewashing is Rs 4 per
square metre, find the :(i) Inside surface area of the dome (ii) Volume of the air
inside the dome
19. A shopkeeper has one spherical laddoo of radius 5 cm. With the same amount
of material, how many laddoos of radius 2.5 cm can be made ?
20. A right angled A ABC with sides 3 cm, 4 cm and 5 cm is revolved about the
fixed side of 4 cm. Find the volume of the solid generated. Also, find the total
surface area of the solid.

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