MENSURATION
(CYLINDER, CONE, SPHERE)
CLASS X WINTER COACHING
SIR DEVEN’S PRACTICE PAPER
ST. ANTHONY’S SCHOOL GIRLS’
1. A hemispherical bowl of diameter 7.2 cm is completely filled with chocolate sauce. The
sauce is poured into an inverted cone of radius 4.8 cm. Find the height of the cone.
Ans: 4.05 cm.
2. The circumference of the base of a 16 m high solid cone is 33 m. Find the volume of the
cone.
Ans: 462 m2.
3. A conical tent has the area of its base as 154 m2 and that of its curved surface area as 550
m2. Find the volume of the tent.
Ans: 1232 m2.
4. It is required to make a hollow cone 24 cm high whose base radius is 7 cm. Find the area
of the sheet metal required including the base. Also find the capacity of the cone.
Ans: Area = 704 cm2, Volume = 1232 cm3.
5. A semi-circular thin sheet of metal of diameter 28 cm is bent and an open conical cup is
made. Find the capacity of the cup. ( Take Π = 3.14)
Ans: 622.3 cm3.
6. From a solid cylinder whose height is 8 cm and radius is 6 cm, a conical cavity of height
8 cm and base radius 6 cm is hollowed out. Find the volume of the remaining solid. Also
find the ratio of the remaning solid and the conical cavity.
Ans: Volume: 603.4 cm3
7. 3 solid balls of metal of radii 8 cm, 6 cm and r cm are melted to form a solid sphere of
radius 9 cm. Find r.
Ans: 1 cm
8. A spherical ball of lead has been melted and made into identical smaller balls with radius
equal to half of the radius of the original one. How many such balls can be made?
Ans: 150
9. A cylindrical container of radius 6 cm and height 15 cm is filled with ice cream. The
whole ice cream is to be distributed to 10 children in equal cones with hemispherical
tops. If the height of the conical portion is four times the radius of its base, find the radius
of the ice cream cone.
Ans: 3 cm
10. A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. The total
height of the toy is 15.5 cm. Find the total surface area.
Ans: 214.5cm2.
11. The diameters of 2 cones are equal. If their slant heights are in the ratio 5 : 4, find the
ratio of their curved surface areas.
Ans: 5 : 4
12. A girl fills a cylindrical bucket 32 cm in height and 18 cm in radius with sand. She
empties the bucket on the ground and makes a conical heap of the sand. If the height of
the conical heap is 24 cm, find:
(i) radius Ans: 36 cm
(ii) slant height Ans: 43.26 cm
13. A solid consists of a cylinder surmounted by a cone at one end, a hemisphere at the other
end. Given that common radius = 3.5 cm, height of the cylinder = 6.5 cm and total height
= 12.8 cm. Calculate the volume of the solid and correct it to the nearest integer.
Ans: 376 cm3.
14. The diameters of 2 cones are equal. If their slant heights are in the ratio 5 : 4, find the
ratio of their curved surface areas.
Ans: 5 : 4
15. A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top,
which is open is 5 cm. It is filled with water upto the rim. When lead shots each of which
is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows
out. Find the number of lead shots dropped in the vessel.
Ans: 100
16. A metal cube is completely submerged in water contained in a cylindrical vessel with
41
diameter 30 cm. The level of the water rises by 1 cm. Find find the side of the cube.
99
Ans: 10 cm
17. Find what length of the canvas 2 m in width is required to make a conical tent 20 m in
diameter and 42 m in slant height allowing 10% for folds and stitching. Also find the cost
of the canvas at the rate of Rs 80 per meter.
Ans: 726 m, Rs 58080
18. A cone and a cylinder are of the same height. If diameters of their base are in the ratio
3: 2, find the ratio of their volumes.
19. The radius and height of a cone are in the ratio 5: 12. If its volume is 2512 cm3, find its
slant height.
20. A tent is 10m high and the radius of its base is 24m, find:
(i) slant height
(ii) cost if 1 m2 is Rs 70.
21. The volume of a cone is 9856 cm3 and the area of its base is 616 cm2. Find:
(i) slant height
(ii) total surface area
22. The total surface area of a cylinder is 6512 cm2 and circumference of its base is 88cm.
Find the volume.
23. the radius and height of a cylinder are in the ratio 2 : 7. If the volume of the cylinder is
704 cm3 , find the total surface area of the cylinder.
24. The circumference of the base of the cylinder is 132 cm and its height is 25 cm. Find
(i) Radius
(ii) Volume
25. If the volume of a cone of height 9 cm is 48 π cm3, find the diameter.
