Curved Surface Area of a Cone
Section A – Calculate the surface area of each cone, based on the information given
a)
b)
c)
14cm
12cm
22cm
30cm
5cm
8cm
Section B – Find the missing value, based on the information given
a)
x
Surface Area =
75.4cm2 (24π)
CAREFUL!!
b)
Slant height = double the radius
Surface Area = 461.81cm2
(147π)
x
20mm
Section C – Longer questions!!
a)
i) A cone has a base radius of r and a slant height of h. Write an expression for the
surface area of the cone.
ii) The base radius is doubled and the height is doubled. Write an expression for the
new surface area. HINT: How could we write the base and height based on the
information given…
ii) What does your algebra show the surface area has changed by?
b)
A sector of a circle is drawn. The radius of
the circle is 9cm and the angle inside the sector
at the centre is 240°. The circle is folded to
make a cone (by pushing the two radii together.)
Calculate the surface area of the cone (include the base)
9cm
240°
Curved Surface Area of a Cone ANSWERS
Section A – Calculate the surface area of each cone, based on the information given
a)
b)
c)
14cm
12cm
22cm
30cm
5cm
8cm
267.03cm2 (85π)
233.23cm2
2224cm2
Section B – Find the missing value, based on the information given
a)
x
Surface Area =
75.4cm2 (24π)
CAREFUL!!
b)
Slant height = double the radius
Surface Area = 461.81cm2
(147π)
x
20mm
10cm
Radius = 7cm so x = 12.12cm (7√3)
Section C – Longer questions!!
a)
i) A cone has a base radius of r and a slant height of h. Write an expression for the
surface area of the cone.
πr2 + πrh
ii) The base radius is doubled and the height is doubled. Write an expression for the
new surface area. HINT: How could we write the base and height based on the
information given…
4πr2 + 4πrh
ii) What does your algebra show the surface area has changed by?
4 times bigger
b)
A sector of a circle is drawn. The radius of
the circle is 9cm and the angle inside the sector
at the centre is 240°. The circle is folded to
make a cone (by pushing the two radii together.)
Calculate the surface area of the cone (include the base)
90π
9cm
240°