Intensive Tutorial Service
Class: 10/SLC
Mathematics Practice Questions
Topic: Mensuration
1. Find the Volume of given solid figures.
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Intensive Tutorial Service
Class: 10/SLC
Mathematics Practice Questions
Topic: Mensuration
2. Find the curve surface area & total surface area of the given solid figure.
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Intensive Tutorial Service
Class: 10/SLC
Mathematics Practice Questions
Topic: Mensuration
3. a) Find the volume of the given solid figures.
Hints: III(a) r = 5cm,
In FIE, EF =
122 + 52 = 13cm
All cones are equal, so height (h) = 12 cm & slant height (l) = 13cm
1
Volume of one cone (V1) = r2 × 12 cm3
3
Volume of cylinder (V2) = r2 × 28 cm3
2
Volume of hemisphere (V3) = r3 cm3
3
2
 V = 3V1 + V2 + V3 = r2 (12 + 28 + × 5 ) cm3
3
b) Find the curved surface & total surface area of the given solid figure.
Hints III (b)
r = 5cm, EI = 12cm, In FIE, EF = 122+52 = 13cm
T.S.A. of one cone (A1) = r (r + 13), T.S.A. of cylinder (A2) = 2r(r+28)
T.S.A of hemisphere (A3) = 3r2, Area of one circle (A4) = r2
T.S.A of whole figure (A) = 3A1 + A2 + A3 - 6A4 = 270 + 430 + 75 - 150 = 625 =
2
1964.28cm
2
C.S.A of whole figure = A
or, 3s1 + s2 + s3 = 3rl + 2rh + 2pr
c) A cone is placed on a cylinder so that the base of the cone covers exactly
the base of the cylinder as shown in the figure. The area of the base of the
cylinder is 125 cm2 and the height of the cylinder is 3 cm. If the volume of
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Mathematics Practice Questions
Topic: Mensuration
the whole solid is 625cm3, find the height of the solid.
d) A cone is placed on a cylinder so that the base of the cone covers exactly the
base of the cylinder as shown in the figure. The area of the base of the
cylinder is 125 cm2 and the height of the cylinder is 3 cm. If the volume of
the whole solid is 625cm3, find the volume of conical part only.
e) A tent is of the shape of right circular cylinder upto a height of 4 cm with
radius 14 cm and then becomes a right circular cone with height of 6 cm.
Calculate the total surface area of tent.
f) A tent of height 33 m is in the form of a right circular cylinder of radius
60 m and height 22 m surmounted by a right circular cone of the same
radius. Find the total surface area of the tent.
g) In the given figure, cone, cylinder and hemisphere of same radius are
joined. Find the ratio of volumes of cone, cylinder and hemisphere.
h) In the given solid, the radii of cone and hemisphere are equal. Find the ratio of their
volumes.
i) A circus tent is cylindrical to a height of 5 m and conical above it. If its diameter is
112 m and its slant height 73 m. Calculate the total area of canvas required.
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Mathematics Practice Questions
Topic: Mensuration
4. a) Three silver metallic sphere of radius 1cm, 6 cm and 8 cm respectively are melted
and form a single new metallic sphere. Find the diameter of that new sphere.
b) Three metallic sphere of radius 2cm, 12 cm and 16 cm respectively are melted and
form a single new metallic sphere. Find the diameter of that new metallic sphere.
c) The diameter of an orange is made one-third of its original size. What will be the
difference in the volume?
d) If the radius of a sphere is doubled, what will be the difference in the volume.
e) A solid iron sphere of radius 3 cm is melted to form a solid right circular cylinder of
diameter 6 cm. Find the height of the cylinder.
f) A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is
melted into a cone of base diameter 8 cm. Find the height of the cone.
Answers
1. a) 11314.28 m3
d) 6146.64cm3
g) 290400cm3
j) 6930cm3
m) 358.27cm3
2.
b) 44869.52mm3
e) 553.13cm3
h) 11314.28cm3
k) 2310cm3
n) 1961.13cm3
c) 4646.68cm3
f) 2614.85cm3
i) 2258.66cm3
l) 1950.66cm3
a) 1980cm2, 1980cm2
b) 314.28cm2, 364.57cm2
2
2
c)804.56cm , 1005.71cm
d) 4604.28m2, 4682.99m2
e) 9208.57mm2,9522.85mm2 f)1551.44cm2, 15551.44cm2
g) 19800cm2, 31114.28cm2 h) 2074.27cm2, 3331.43cm2
i) 985.6cm2, 985.6cm2
j) 858cm2, 858cm2
k) 282.85cm2, 282.85cm2
l) 829.71cm2, 829.71cm2
a) 3404.74cm3
b) 625cm2 or 1964.28cm2, 625cm2 or
1964.28cm2
c) 9cm d) 250cm3 e) 1020.8cm2 f) 19800m2 g) 1:3:1 h) 6:7
i) 14608m2
j) 9 cm
k) 36 cm
26
4. a) 9cm b) 18cm c)
times of original volume
d) 7 times of original volume
27
e) 4cm
f) 14 cm
3.
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