VOLUMES OF SOLIDS
Volumeprism = Areabase x heig
A . Volume of a Prism
Page 1
Volume (cylinder) = πr
3 . The cylinder - a special prism.
Calculate the volumes of the following cylinders:
(a)
8 cm
3 cm
(b)
(c)
2 5 cm
10 cm
9 5 cm
13 cm
15 cm
(d)
(e)
2 cm
6 5 cm
1 metre
1 cm3 = 1 ml ;
4 . Remember:
1000 cm3 = 1000 ml = 1 litre
How many litres of water will the following drums hold?
(a)
25 cm
(b)
40 cm
(c)
60 cm
40 cm
55 cm
35 cm
7 cm
5 . A cylindrical tin of Maxcafe Coffee is 10
centimetres high and has a base diameter
of 7 centimetres.
What is the volume of coffee in the tin
when it is full?
Page 2
10 cm
80 cm
7 . Meanz Beanz tins are packed into this cardboard box.
(a) How many tins can be placed on the
bottom layer?
8 cm
M
B
33 cm
11 cm
(b) How many layers will there be?
(c) How many tins can be packed in
the box altogether?
(d) How much air space in the box is
there around all the tins?
32 cm
48 cm
8 . This cast iron pipe has an internal diameter of 16 centimetres and an outside diameter of 20
centimetres. The pipe is 1 5 metres long.
16 cm
20 cm
15m
Calculate the volume of iron needed to make the pipe.
9 . How much liquid feeding will this
semi-cylindrical pig-trough hold?
18 cm
120 cm
Page 3
B . Volume of a Cone
Volume (cone) =
11 πr2h
3
Exercise 2
1 . Calculate the volumes of the following conical shapes:
(a)
(b)
(c)
10 cm
15 cm
6 cm
(d)
18 cm
7 cm
3.5 cm
(e)
16 cm
10.8 cm
40 cm
12 6 cm
6 cm
2 . The wafer of an ice-cream cone
has a diameter of 6 centimetres.
The cone is 10 centimetres high.
Calculate the volume of the cone.
10 cm
3.
The 'sloping' height of this cone is 26 cm.
The base radius is 10 cm.
26 cm
(a) Calculate the height of the cone.
(b) Calculate the volume of the cone.
10 cm
Page 4
4 . Calculate the total volumes of the following shapes.
(a)
(b)
30 cm
25 cm
20 cm
30 cm
40 cm
30 cm
18 cm
40 cm
5 . Water is poured into this conical flask
at the rate of 50 millilitres per second.
12 cm
(a) Calculate the volume of the flask.
(b) How long will it take, to the nearest
second, to fill the flask to the top?
24 cm
Page 5
C . Volume of a Sphere
Volume (sphere) =
4/ πr3
3
Exercise 3
1 . Calculate the volumes of the following spheres:
(a)
(b)
(c)
11 cm
9.2 cm
6.5 cm
(d)
(e)
10.4 cm
30 cm
2 . This football is fully inflated.
Calculate the volume of air
inside the football.
24 cm
3 . Calculate the volumes of these two 'hemispheres':
(a)
(b)
14 cm
8 5 cm
Page 6
4 . (a) Calculate the volume of water which can be
stored in this copper hot water tank in cm3.
The tank consists of a cylinder with two
hemispherical ends.
40 cm
(b) How many litres of water will it hold?
(1cm3 = 1 ml; 1000 ml = 1 litre).
5.
60 cm
Calculate the volume of this child's
rocking toy which consists of a cone
on top of a hemisphere.
11 cm
7 cm
18 cm
6 . This decorative wooden fruit bowl
is in the shape of a hollowed out
hemisphere.
16 cm
Calculate the volume of wood required
to make it.
Page 7
Checkup for Volumes of Solids
Vol (cylinder) = r2h
Vol (cone) = 1/3r2h
Vol (sphere) = 4/3r3
3 . Calculate the volumes of the following shapes:
(a)
9 cm
(b)
15 cm
11 cm
(c)
10 4 cm
7 cm
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